Section 8604 is authority for the general proposition that a child having a presumed father cannot be adopted without the consent of the child's birth parents, if living. ( 8604, subd. (a).) However, subdivisions (b) and (c) of the statute also set forth an exception to the general rule: "(b) If one birth parent has been awarded custody by judicial order, or has custody by agreement of both parents, and the other birth parent for a period of one year willfully fails to communicate with and to pay for the care, support, and education of the child when able to do so, then the birth parent having sole custody may consent to the adoption, but only after the birth parent not having custody has been served with a copy of a citation in the manner provided by law for the service of a summons in a civil action that requires the birth parent not having custody to appear at the time and place set for the appearance in court under Section 8718, 8823, 8913, or 9007. "(c) Failure of a birth parent to pay for the care, support, and education of the child for the period of one year or failure of a birth parent to communicate with the child for the period of one year is prima facie evidence that the failure was willful and without lawful excuse." Section 8604 permits an adoption to proceed without the consent of a parent who has willfully failed to communicate and support a child for one year. It does not purport to relieve that parent from any further obligation to pay child support. Such relief is provided, if at all, when the adoption is consummated. Under section 8617, "The birth parents of an adopted child are, from the time of the adoption, relieved of all parental duties towards, and all responsibility for, the adopted child, and have no right over the child."