Lists of Lists management

I have, currently, a list of multiple lists of points across curves.  That's a bit confusing, let me see if i can explain it differently:

List of curves [ (list of points on curve A)

                     (list of points on curve B)

                     ....

                     (list of points on curve X)]

Is there any way to create a new list of lists from individual indices of these lists? IE can I extract all list items at index 0 on each list and put them into a new list.  Then do the same for index 1, 2, 3, 4, etc?

I've tried a few clunky solutions but right now I'm just throwing stuff at the wall to see what sticks.