In addition to Clerk's comments - talking about parental "rights" is generally a mis-nomer. It's the rights of the CHILD that the courts care about - including the right to financial support of two parents, and the right to know who BOTH parents are, and to form relationships with BOTH. It's easy for a parent to give up their "rights", simply by choosing not to exercise them; but such choice doesn't negate the rights of the child, which the court will look out for - and in CA courts are willing to do so for the child's entire life as a minor.
Yes, you're missing the fact that CA no longer allows you to name some random man as the father of your child. Since about 1996.
Okay, must be confusing with another state or something.
So couldn't a woman who doesn't want a man to be in the childs life, lie about not knowing who the father is?
I mean, either way, if a mother named a random guy or didn't name anyone, the guy could always get a paternity test to prove yes or no... isn't it the same?
Let's try this again. Once more, with feeling.
A woman can no longer name random people as the father of their children. The only person's name who automatically is entered onto a child's birth record is the HUSBAND of the woman. Otherwise, the only way a man's name is entered onto a child's birth record is by (1) a man signing a Declaration of Paternity or (2) the court establishing paternity.
A DNA test is NOT required for the establishment of paternity, not even judically - and there are VERY FEW STATES (in fact, I can't think of one) who allows you to just name a man as the father of your child anymore.