(1) A parent or guardian whose consent to the adoption of a child is required may relinquish to the department or an agency all rights with respect to the child, including legal and physical custody and the right to consent to the child's adoption.
(2) A parent or guardian whose consent to the adoption of a child is required and who has filed a notice of parental placement under 42-4-103 for a direct parental placement adoption may:
(a) relinquish to the prospective adoptive parent all rights with respect to the child, including legal and physical custody; and
(b) consent to the child's adoption by the prospective adoptive parents.