The recipes I cook usually use either butter or 1-2 tablespoons of olive oil. With butter, everything is fine and the pan gets an 'even' coating of small droplets of fat. But whenever I use olive oil, it tends to all form a single big puddle at the edge of the non-stick frying pan, even if I empty the measuring scoop in the middle of the pan. One of those puddles recently splashed when I added vegetables to the pan, and I burned my finger quite badly, so I want to prevent something like it from happening again. I found this post asking why oil does this, and the answer there gives some ideas on what to do, but the circumstances there aren't really applicable: I checked and my frying pan is level which makes sense as the butter also doesn't run off to the sides. Also, I've been using my frying pans for close to a year now, so more than the 'few months' the answer there mentions as being needed to build up damage and allowing oil to spread more evenly. So neither of the two things mentioned there already seems like a possible solution for me. How do I prevent my olive oil from forming a single puddle at the edge of a frying pan? 
Generally this shouldn't be too much of a problem; by moving food around once it is in the pan you will naturally spread the oil across both the food and the pan. You can also use a spatula to spread the oil a little before putting the food in, and tilting the pan to get the oil to run to the far side also helps. If the puddle of oil is significantly splashing you that might be a sign there is too much oil for what you need, but you can also reduce splashing by gently lowering food in (possibly using tools like a spatula or tongs) and putting the side closest to you in first so that any splashing is away from you. 