How does the law apply to custody of unborn children?

What if a pregnant mother leaves the state, then files for temporary custody in the new state? This isn't just a hypothetical question, it's being played out in a custody battle in New York state between an Olympic skier and his girlfriend.

Article here.

The legal question is whether the Uniform Child Custody Jurisdiction and Enforcement Act gives courts authority to determine the custody, or jurisdiction of custody cases, based on the location of the pregnant mother. The tabloid question is who gets to raise baby Samuel Bode Miller-McKenna -- son of Olympic downhill ski legend Bode Miller and a former Marine he met through a "high-end" match-making service -- and where. The New York Times covers the story in "Custody Battle Raises Questions About the Rights of Women."