Well if iam not mistaken he can if he wanted to sign off his parental rights and that will in many ways leave him with no obligation to pay child support or have visitations. It is something if he does do it, and later on decides he wants to have some type of bond with child, it will be harder to reverse. It would actually be set in stone. But then it would leave an open door for your daughter should she meet someone and marry and that person has cared for the child, they can then go forward with adoption as long as she keeps the document of the other person legally terminating parental rights.

