What does an assisted one-legged squat do?

I do one-legged squats ( also called pistols) and I hold on to something such as the door frame in order to make it easier. I used to do it without holding onto anything but falling over started to really piss me off. I am assuming that assisting myself would eliminate the use of core muscles. So what does an assisted one-legged squat work out? Would it just work out the glutes, the quads, and the hamstrings?

It isolates your quads just like concentration curls to the biceps.