Legal Question in Family Law in California

You cannot sign away your parental rights except in a step-parent adoption. If your child is adopted by another man, then you are free of all rights and obligations, including child support.

A declaration terminating parental rights does indeed terminate all parental rights and responsibilites (CA Fam Code $7803), however this does not affect any support arrears.

A petition to terminate parental rights can actually be brought for any of the following: a) Abuse of parental authority (action by minor or relative within the 3rd degree); b) abandonment; c) neglect or cruelty; d) parent is suffering from substance abuse or moral depravity; e) parent is convicted of certain felonies or was conceived under certain felonious acts; f) parent is developmentally disabled or mentally ill, or mentally disabled; g) under certain conditions, if the child becomes under the supervision of the juvenile court; or h) private or public adoption.

You may voluntarily sign away most parental rights by agreement, however in that case, you will not be terminating your rights and therefore will still be required to supply support for your minor child.