Legal Question in Family Law in California

Yup.

She may disappear, but there are complex legal issues here. Is this a homework assignment, or an actual case?

Because you state the parties lived together, I assume they were never married. With the exception of the marriage, all of the other facts are identical to the situation in In re Marriage of Buzzanca. ((4th Dist. 1998) 61 Cal.App.4th 1410.) In that case, a husband and wife agreed to have an embryo unrelated to either of them, artificially inseminated and implanted in a surrogate. After the pregnancy, the husband filed for divorce. In a bizarre ruling, in a difficult case, the trial judge ruled that the baby had no legal parents. On appeal, the 4th District Court of Appeal reversed. The Court of Appeal held that because the baby was born at the request of the infertile married couple, they were the legal parents of the baby.

It is not clear, however, whether this would extend to a situation involving non married partners.

There is another doctrine, known as parentage by estoppel that may interplay. If the man held himself out as the father, and received the children into his home, he may be estopped to deny paternity later.