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The answer is yes. However, the parent that is voluntarily giving up parental rights does not also void the duty to pay child support if they have to, UNLESS, the child is being adopted.
For example: A and B have a child and they divorce. B pays A child support. A marries C. C wants to adopt the child. If so, then B can give up their parental rights and will not have to pay child support once C adopts the child.
But: A and B have a child and they divorce. B pays A child support. B wants to give up parental rights. Even if B does, B will still have to pay child support if A demands it.
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