Professor Lori Andrews opines here. Most notably:

The Savages say that their doctor told them that if they didn’t abort, the law would require her to give the child over to the other couple. But, frankly, the law is not that clear. In many jurisdictions, the child born to a woman is the legal child of that woman and her husband, no matter who the genetic father is. There is even a Supreme Court case that holds that a married woman’s lover cannot sue for visitation rights to his child; the child belongs instead to the married couple. (Michael H. v. Gerald D, 491 U.S. 110 (1989)).