Can the father of my child voluntarily sign all rights of our child over to me?

In Louisiana, one cannot "sign over" his parental rights, unless it in a proceeding filed by the state to terminate his parental rights or in an adoption proceeding. He can voluntarily give you sole custody of the child, but he would still have parental rights. For instance, he could sign to allow your husband to adopt your child. I handle adoptions throughout Louisiana.