This is my aloe vera plant. It’s healthy but it long outgrew the 10” pot. Instead of moving it into a bigger pot, I would like to transplant it into 2 or 3 pots.
How should I do this without hurting the plant?
Basically, it looks like you have a dead "parent" plant and several large "children".
It's not very clear from the pictures how many children there really are but I suspect more like 6 or 7 than two or three.
Each "child" will have started growing from the base of one of the old (pretty much dead) leaves. You should be able to gently pull it way from the parent plant. Since the parent is beyond saving anyway, you can cut its leaves off one at a time working from the outside inwards, if you can't see where the "children" are growing from.
It doesn't matter if the "children" don't seem to have any roots of their own. If you plant them straight into a new pot they will soon root and start growing.