Shoudn't have to break much below parallel when doing squats. If people prefer going all the way down, good for them. The ham's can be involved more, but for quad development arse to the ankles is not needed. On the other side; I've been to a few coaches clinic's where they say that stopping at or a little below parallel is dangerious (there terms, not mine) to the whole knee structure. And can set you up for serious injury with too much tension directed to the knee joint(s). Interesting in any case, but I still break a little below parallel.
Those one legged squats can be a killer when first adding them to a workout. Can do them on a high bench, box, etc, where the leg does not have to be held out in front. Lot's of athletes do step-up as an added thigh workout, not to be confused with one legged squats. Step-up are a great exerise to add to anyone's training plan. Good Luck.