Many, many sociopaths fight for custody of their children. Sociopaths are incapable of loving anyone, including their children. So why do they want the kids?
One big reason is to torment the other parent by depriving them of the kids.
Another reason is to make money. If the sociopath is the custodial parent, the other parent will have to pay up until the children are 18, or even older, for kids who go to college.
Child support payments are often determined by the courts. New research shows that the formulas courts use to set the support payments may overestimate the cost of raising a child by 200% to 400%. See this video produced by DivorceCorp.