I have a stepbrother here in NC who did that with his five children, don't know what he did, but as for Cali., probably have to ask a lawyer up in there. As for myself, I paid child support for a little over 15 years and my children didn't want and still don't want anything to do with me, but they are my children and I love them with my life no matter what they think of me.
In most cases, signing over parental rights doesn't relieve you of your financial obligation unless the other parent agrees. However, if the rights are being relinquished to facilitate the adoption of the child, the court will in most cases dismiss child support obligations. Talk to an attorney for professional legal advice.