Except as otherwise provided in the Nebraska Indian Child Welfare Act, the Department of Health and Human Services, or its duly authorized agent, may consent to the adoption of children committed to it upon the order of a juvenile court if the parental rights of the parents or of the mother of a child born out of wedlock have been terminated and if no father of a child born out of wedlock has timely asserted his paternity rights under section 43-104.02, or upon the relinquishment to such department by their parents or the mother and, if required under sections 43-104.08 to 43-104.24, the father of a child born out of wedlock. The parental rights of parents of a child born out of wedlock shall be determined pursuant to sections 43-104.05 and 43-104.08 to 43-104.24.