The canon novel " Aftermath: Life Debt" identifies the remains of Alderaan as a debris field named the Alderaanian Graveyard : Asteroids tumble through space.
They drift and spiral, and when one hits the perimeter shield, it breaks.
Bits drift, pulverized, as the rest of the rock pirouettes away to join the rest of its crumbling brethren.
Every time it happens, it hurts Teven Gale's heart.
Because that asteroid is a piece of his world.
Was a piece of his world, anyway.....
Out in the black, demo-droids drill and dig into the asteroids, one by one
- they look like fireflies out there with their bright-orange light flickering from their cutting lasers.
Those droids look for anything of note from the world the Alderaanians lost: artifacts, remains, fragments of precious stones or minerals or metals.
Even a single brick would be a find.
Accessing any of this wasn't even an option under Imperial rule; the Empire blockaded all access to the Alderaanian graveyard .
--
Interlude:
The Alderaan Flotilla
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Vader was apparently not averse to giving away bits of the former Alderaan as a reminder to unruly systems that they needed to remain loyal to the Empire Darth Vader:
Annual #01
As to what's left, we can actually see it in A New Hope.
In short, not a lot.
"We've come out of hyperspace into a meteor shower or some kind of asteroid collision"
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I'd doubt if there'd be many survivors to populate it.
Basically you'd be left with a huge Asteroid Belt.
It might be worth mining but not likely to have a permanent population unless there are a lot of people who care to live in hollowed-out Asteroids.
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I presume the remains eventually formed an asteroid belt around the star.
The explosive force would rip any atmosphere from the debris; only Alderaanians off-world could survive.
Reassembly of the planet would be unlikely, as the explosion would scatter a substantial fraction of the planetary mass too far to coalesce by gravity alone.
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Referring to Valorum's answer, there was a similar event also in a Legends comic book Star Wars 86: The Alderaan Factor .
A stormtrooper was carrying a chunk of rock around his neck, which was, as he claimed, everything that was left of the planet Alderaan.
Later, the trooper was shot dead and the rock remained in Leia's hands.
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In Star Wars Episode 4: A New Hope, the Death Star destroys Alderaan, killing all life on the planet.  After its destruction, I assume there was still  some  debris left from it being destroyed.  So what happened to this left-over rock and other debris of Alderaan after its destruction by the Death Star?  Was it left alone? Were the remains of Alderaan reinhabited by surviving Alderaanians? Was there some attempt (possibly using some sort of gravity creating device) to recreate Alderaan?
What happened to Alderaan after its destruction by the Death Star?
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Whilst it is never clearly stated whether anything in particular happened to the remains of Alderaan, it is quite likely that nothing happened to them and that Alderaan simply became a large asteroid belt and there would be very few, if any, Alderaanian survivors. The debris from the destruction of Alderaan is now a widely scattered asteriod belt - too diffuse to form a new planet and therefore unable to provide a viable habitat for any surviving Alderaans, even assuming there were enough of them to re-populate it.
All that remains of Alderaan is a debris field tumbling through space, access to which is blockaded by the Empire. Not a lot. It is unlikely there would be many survivors, and anyway all that's left is an asteroid belt which is too widely scattered to coalesce into a planet again and which would not therefore form an attractive habitat for them. All that's left is a small chunk of rock taken from a dead stormtrooper and now in the possession of Leia.