Legal Question in Family Law in California

You cannot sign over your parental rights unless the child is being adopted. Once the adoption is complete, you would not owe child support. Until then you do.

There is no such thing as signing over your parental rights. Agreements between parents that one parent does not have to pay child support are unenforceable. Only adoption or an order from dependency court terminating your parental rights would sever your duty to pay child support.