I have been thinking about this and I am sure that to do it legally you need an order from the family court. We are talking about the natural parents giving up all responsibility for their own child , and I don't think the court would allow it unless there was an overwhelming reason for it. The family court CAN ONLY MAKE ONE POSSIBLE DECISION in any case dealing with the care of a child/children and that is to do
' 'Whatever is in the best interest of the child' '
no other ruling is even possible. The child's interest overrides all other considerations.
You do not say why you want to do this and I am sure you have your reasons for that. But, to get sole guardianship , you and the parents will have to put your case to the family court and abide by whatever they decide to be in the child's' best interest. It may not be the decision you hope for. A child is not property like a car for example that can be given away if you want to. When the child is 10 the court will ask the child what he or she wants to happen. They are not compelled to go with the child wants but from age 10 the child's wishes / views must be taken into consideration.