What makes me so sad about the entire situation is that there is a child that could eventually be used as a pawn. My sincerest hope is that Alexandre will be allowed to grow up in peace with support (material and emotional) from all parents biological and other.
I have a feeling that PA would never try to take full custody as long as Nicole wasn't endangering the child in any way. A court battle would thrust Alexandre into the spotlight and undermine any gravitas as a head of state that Albert would be trying to cultivate. He will probably be treated by Albert's legitimate family, should he have one, as a cousin more than a sibling. Alexandre is set for life; he will probably have a trust fund that he will slowly gain control of as his 20's and 30's progress (with a corporate trustee, I imagine) and right now, as he is recognized by PA, he has equal rights to his father's fortune as any legitimate heir would have.
I think Kanye West wrote a song that fits Nicole, crisinaki.