RIVER WILD | Holly Branson touring her father's private game preserve at Ulusaba, Virgin's unofficial South African headquarters. (Belstaff sweater, $595, belstaff.com, DKNY pants, $215, Bloomingdale's) Photography by Ambroise Tezenas

NOT SO MANY YEARS AGO, Holly Branson would never have imagined she'd be where she is this muggy afternoon—listening to a bunch of South African kids pitch their ideas for start-up businesses to a panel of mentors at the Branson Centre of Entrepreneurship in Johannesburg. The kids, fighting varying degrees of stage fright, aren't worried so much about the center's tough-minded mentors—they're used to that. This is a different kind of pressure. Holly Branson is here, and in South Africa the Bransons are royalty.

Afterwards, there is a mild stampede as everyone crowds around to take a picture with her. Holly, 31, graciously poses with all comers. "I realize I'm a new face of the brand, and it's a role I accept now," she says. "I know how excited people are to have the family there." And then she drops the bombshell—or at least it would have been a bombshell to her slightly younger self: "Yes, it's logical for me to think of running the company one day." Wait a beat. "But not for many years. My dad isn't slowing down. If anything, he's speeding up."

Her dad is Sir Richard Branson, the man who built the Virgin brand and a $4.6 billion fortune with a combination of pluck, music-hall antics, common sense and daredevilry. (At 63, he's still at it: Branson's Virgin Galactic is currently flight-testing vehicles that will launch the first paying tourists into space; Richard himself will be on the first flight—and later, Justin Bieber, who recently bought a ticket.) There was no getting away from her father's exploits when Holly was growing up. "Dad was always working in the living room. There was no distinction between work and life—it was the same thing."

Who wouldn't want to be a part of all that? Well, Holly Branson for one. She had a different dream. "I always knew I wanted to be a doctor. I saw a lot of my friends having a hard time figuring out what they wanted to do, so I'm glad I had a purpose and goal to focus on. I liked the discipline and the sense of structure." Her single-mindedness kept her in something of a cocoon while her father was off ballooning across the Atlantic. He teased her about it. "When I brought my medical school friends home, Dad used to tell us that we didn't know anything about the world. He started giving me impromptu quizzes about history and current events. I quite liked that."

THE LONG VIEW | Holly with her father on the deck of Ulusaba's Rock Lodge. 'She won't do any wing-walking, like I did,' says Sir Richard Branson. 'She'll do it her own way.' Photography by Ambroise Tezenas

Holly got her medical degree in 2007 and worked for a year in the neurology department of Chelsea and Westminster Hospital as a Junior House Officer. By then the glamour of life in hospital scrubs had worn off. That's when she decided to take a year off.

"It was my dad who said, 'Well, why don't you come work at Virgin,' " recalls Holly. "I did internships at all the businesses, and at the end of the first year I thought, Oh, I'm just not ready to go back. By the end of the second year, it was clear I was never going back."

It wasn't a seamless transition. Holly started out shy and unsure, shaky on the rudiments of business and not naturally keen on mastering them. "I'm taking courses in it, but I don't much like numbers," she confesses. Like her father, however, she's a plugger. She's already filled some of the holes in her business resumé, and she will surely end up filling the rest.

"She's got on and done it," says her father proudly. "She's already learned a lot more about the world than she would have as a doctor. Now she's going out on her own. She won't dress up in funny clothes or do any wing-walking like I did. She'll do it her own way."

Officially, Holly is listed as special projects manager at Virgin Management Limited. She also sits on the board of Virgin Unite, the incubator for the many nonprofit enterprises that occupy most of Richard's time and energy these days—a mix of causes that includes fighting fistula, enlisting notables like Desmond Tutu and Kofi Annan to tackle human rights abuses and promoting fuel-efficiency in the shipping industry, among many other things. Virgin Unite has the throw-it-against-the-wall zeal that characterizes Richard's for-profit business ventures, and like them is also underpinned by the conviction that a little entrepreneurial moxie can move mountains.

Unofficially, however, given the nature of Virgin's far-flung enterprises, Holly's role is destined to get much bigger. Richard's management style has suited his strengths: manic energy, wild-eyed enthusiasm and a taste for kicking corporate Goliaths in the shins. On the other hand, it takes an icon to represent some 400 companies with the same brand, most of which have nothing to do with each other except that he felt like founding them. Richard knows this, of course, and he knows, too, that sooner or later, there will be a job opening for a new icon. Which is where Holly comes in (and perhaps her younger brother, Sam, who is 28).

HELPING HANDS | Holly with local villagers at a new day care center. Photography by Ambroise Tezenas

"When Steve Jobs died, Apple lacked a great deal not having a personality to keep that brand going," says Richard. "Virgin is the number-two or number-three most respected brand in the world, and it helps to have a powerful personality to get that brand out there. If I get run over by a truck tomorrow, Holly will be in a position to do that."

The dynastic symbolism was evident to anybody who watched the 2010 London Marathon. Holly, dressed in a caterpillar costume, roped herself to 33 other caterpillars to break the roped-together marathon record as a charity stunt. Richard ran alongside dressed as a bright red butterfly. Get it?

The marathon ultimately led Holly and Sam to start the Big Change Charitable Trust with some of the other caterpillars who ran with her, like Prince Andrew and Fergie's daughter Princess Beatrice. They are tomorrow's do-good royalty, and Holly is already thinking of ways to harness the billions they will one day inherit.

A little over two years ago, Holly met Craig Kielburger, who had founded a charity called Free The Children in Toronto in the mid-'90s, when he was just 12 years old. The organization has since built over 650 schools internationally and channels funds toward health, sanitation and agriculture projects in eight Asian, African and Latin American countries through its Adopt a Village program. Holly forged a partnership between Free The Children and Virgin, which funnels some of the money it collects from donations on Virgin Atlantic flights. In March 2014, Free The Children will organize its first big event in England, called We Day UK. Holly is its cochair and prime mover.

"From our first conversation, Holly ended up joining us while we were constructing schools in Kenya and India," recalls Kielburger. "Chiselling walls, mixing gravel and cement—backbreaking work. She may be a Branson, but she doesn't mind rolling up her sleeves. If you ask her what she really enjoys, it's raising a roof. She's less comfortable calling people for funding, but when she calls, people answer, and that's the greatest good she can do. Without her, I'm not sure we would have had We Day UK. She's become more certain as she's accepted this role."

Zebras at Ulusaba game preserve Photography by Ambroise Tezenas

I meet Holly and her husband, Freddie Andrewes, at Ulusaba, the Bransons' plush game lodge near the border of South Africa's Kruger National Park. Holly is here as part of a Virgin Unite Connection trip, during which she and her father will meet with business leaders interested in incorporating innovative philanthropy into their practices. She's tall and athletic with bright eyes, a persistent smile and an easy, unflappable way about her. Her father doesn't think that part comes from him. "My wife, Joan, is a working-class Glaswegian from a poor family, and she's very down to earth—the complete opposite of me," says Richard. "I think the kids have a lot of her attributes."

"The men in my family are criers. Sam's more emotional, I'm more analytical. If we ever run Virgin, I think we'd make a pretty good team."

—Holly Branson

Holly and her husband make an appealing couple. He's a big chap with a ruddy, open face and a very firm handshake. The two were high-school sweethearts and kept going despite a few break-ups—Holly says they would never have made it if they hadn't tasted life apart. Andrewes used to be a ship broker, but he got tired of it (and it didn't give him enough time with Holly), so a few years ago he joined the investment team of Virgin Group. "Everyone asks if we talk about work when we get home, but it's not work to us," says Andrewes. "It's a family business. We talk about it all the time."

Ulusaba means "place of little fear" in the local language, because it occupies a tall hillock from which you can scan the countryside for miles around. Today, it does double duty as Richard's unofficial South African headquarters and an exclusive hotel in Virgin's portfolio—Branson has a knack for mixing business and pleasure. Thatched villas perch on the rocks overlooking a small lake where hippos snort and elephants sip.

When I visit, the whole clan is here, which is not uncommon. They arrange their lives to spend as much time in each other's company as possible. This time, they are all here for a reason. Sam is getting married to his longtime girlfriend, Isabella Calthorpe, whom everybody calls Bellie. Sam makes documentary films on serious subjects like drug policy, but he's already got one foot in the family business, and everyone is just waiting for the other foot to follow.

Holly greets a child at the center. Photography by Ambroise Tezenas

At dinner, talk turns to Sam's upcoming nuptials. He cried at Holly's wedding, and he's nervous he'll lose it at his own. "I don't mind, really, but I don't want to get all, I love you sooo much!" Sam says, fake blubbering. "My father cries at anything, particularly when he's happy." Holly says she takes after her mother, and Richard's mother, Eve, too. Eve was the no-nonsense one who stiffened Richard's spine: The story goes that she once took young Richard out to the countryside and left him to find his way home alone. His father, Ted, was the softie who gave everyone unlimited license to hug, which Richard indulges frequently during dinner.

"The men in my family are the big criers," says Holly. "Sam's more emotional, I'm more analytical. I think if we ever run Virgin, we'd make a pretty good team."

The Bransons have added an eighth deadly sin of their own to the other seven: sitting still. Nobody does. Every day starts at 5:30 with a game drive, and nobody begs off except me. "You're really not very adventurous, are you?" says Richard, eyeing me warily. The next two days are a whirlwind of drive-bys, handshakes and photo ops. Free hearing aids are fitted to local villagers at a nearby clinic, Bhubezi Community Healthcare. At a different village, a new day care center is getting ready to open, and furniture needs to be moved in. It's hot and humid, and then the next day the rain comes streaming through the jury-rigged tarps on the roofless Land Rovers. Through it all, Holly never loses the kind of bulletproof cheerfulness you see in English World War II movies. "Great fun" is a phrase the Bransons say often, and it seems to apply to anything from a picnic to an earthquake. If your ship goes down, you'd want a Branson—any Branson—in your lifeboat.

Holly will probably have children soon. Now that Sam's getting married, perhaps they can collaborate on a tribe of cousins, like the nine she grew up around. That could shake things up. There's always a tension between the words "family" and "business," especially when you put them together, and Richard feels it keenly. His mother left work to stay home and raise her children. His wife, who mostly stays at the Branson home on Necker Island in the Caribbean, is the invisible rock that anchors everybody.

"She's a full-time mom even now," says Richard. "It's a question mark how it will affect things when Holly has children. In trying to map out succession plans, a lot of wonderful things could get in the way."