Once a petition to terminate parental rights has been filed, the parent of a child adjudicated as a dependent child shall thereafter be without authority to affect the custody of his or her child except such parent may:
(1) Consent to a judgment terminating his or her parental rights; and
(2) Execute an act of surrender in favor of:
(A) A third party if all of the parties to the petition to terminate parental rights agree; or
(B) The department.