(1) A parent, an *alleged father, the department, or an agency may file with the court a petition to relinquish a child to the department or an agency. The parent's or *alleged father's written consent to adoption shall accompany the petition. The written consent of the department or the agency to assume custody shall be filed with the petition.
(2) A parent, *alleged father, or prospective adoptive parent may file with the court a petition to relinquish a child to the prospective adoptive parent. The parent's or *alleged father's written consent to adoption shall accompany the petition. The written consent of the prospective adoptive parent to assume custody shall be filed with the petition. The identity of the prospective adoptive parent need not be disclosed to the petitioner.
(3) A petition for relinquishment, together with the written consent to adoption, may be filed before the child's birth. If the child is an Indian child as defined in 25 U.S.C. Sec. 1903(4), the petition and consent shall not be signed until at least ten days after the child's birth and shall be recorded before a court of competent jurisdiction pursuant to 25 U.S.C. Sec. 1913(a).