What forms do you need to sign over your parental rights?
The parent would need to file a petition for the voluntary termination of parental rights (TPR) in the state court that has jurisdiction. After filing the petition a hearing date would be set and the judge would listen to the reasons for the request and allow any interested party to contest the action. TPR's are generally granted so that the child/children can become eligible for adoption, not for a parent to escape their financial obligations to their minor children.
There must be a court order terminating parental rights. A person cannot sign over their rights to another -- the law does not recognize such a procedure. Until the court issues an order, the father has retained their parental rights, and child support payments will need to continue according to the court order. If parental rights are terminated, there are no child support payments required