In California if a mother is on welfare and the father signs all rights of the child over to the mother to stop child support does welfare get shut off for the mother?

No as he can't do that. Not even the courts have the authority to exempt the man from paying child support when Welfare is involved. The mother has no say or authority over the child support. She forfeited that right when signing up. She would have to first give up her claim to Welfare benefits before any action could be taken on child support.