I'm Doug, and I'm very sorry to hear of your family's situation. My goal is to provide you with excellent service today. I am a licensed CA attorney.
While the mother-to-be may say that she wants nothing, there is no reason to believe that she will not change her mind. There is nothing that your son can sign or do that will eliminate his future liability for child support.
If she files for welfare such as food stamps or Medicaid/MediCal for the baby, the state will immediately file for child support to be ordered against your son. She also may change her mind at any time and ask a court to order child support---even retroactive child support if he goes for several years under a private agreement before she decides she wants support.
Only, if after the baby is born, the child is adopted by a stepparent or a couple that the mother gives the baby up for adoption to will your son be safe from child support.
Your son needs to prepare himself for the obligation to pay support for this child. Even their attempt to sign away your son's rights will not protect him from child support unless a court actually rules that his parental rights are terminated. And the court will not do that except in exceptional cases---typically where the parent is found to be unfit, or in the event of an adoption.
I understand that you may be disappointed by the Answer you received, as it was not particularly favorable to your situation. Had I been able to provide an Answer which might have given you a successful legal outcome, it would have been my pleasure to do so.
If you have additional questions, you may of course reply back to me and I will be happy to continue to assist you further until your questions have been answered to your satisfaction.
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Thank you in advance. I wish you the best in your future,