But if he gave up his parental rights, wouldn't that release his obligation of paying child support? I don't know, am just curious?
No, in the State of California he would still be obligated to pay child support for his child
once paternity was established, regardless of whether or not he wanted to be a part of the child's life. The hiccup is that, in the State of California, CL could not be established as the father as long as EC was married to someone else. "By law, a man is presumed to be the legal father when he is married to the mother at the time the child is conceived" so, as long as EC remained in California, CL would NOT have been responsible to pay child support, health insurance, military benefit, etc. on their child, once born, unless Erin divorced JC and then established paternity or without a declaration from the court.
Question: Why is it important to establish paternity?
Answer:
If you don't establish paternity, your child will not be able to get child support or health insurance. Establishing paternity as soon as possible makes collecting child support easier in the future. Also, establishing paternity grants the child rights to certain social entitlements, such as social security and pension, and /or
veterans benefits, inheritance protection, and access to family medical records. It is also necessary to establish paternity before custody/visitation can be established.
Question: I am separated from my husband, but not divorced yet. Can my boyfriend, who is the baby’s biological father, sign the Declaration of Paternity?
Answer: No.
The law presumes that as long as you are legally married, the husband is the father of the baby. Only the court can establish paternity with someone other than your legal husband.
Only unmarried women can sign the Declaration of Paternity.
Question: Can a father that is married sign a Declaration of Paternity for a child he fathered outside of the marriage?
Answer: Yes. The father, although married to someone else, can sign the Declaration of Paternity to have his name entered on the child’s birth certificate as the legal father. However,
the mother must not be married because only unmarried women can sign the Declaration of Paternity.
http://hss.sbcounty.gov/DCSS/faqs/faq_paternity.aspx