Need advice - husband left U.S. & I'm carrying our child

I am an American citizen and my husband is a British citizen. I secured a visa for him to come into the States as my fiance' and after we married, we filed for adjustment of status for him. He left our marriage and the country while the application was pending and knowing I was pregnant with our first child. He also knew he would be in violation of his visa requirements. He said when he left that he intended to divorce me and that he wanted the child adopted into another family at birth. However, shortly after his return to England, he said he didn't want a divorce and that he wanted to come back, but since has made little effort (he must secure at least a temporary visa to re-enter). He has never expressed any real interest in the baby, but within the last week has said he suddenly wants custody. I need to start the divorce process and I would like the have full custody of the child. My husband is very attached to his mother and under her influence and she is aggressive about the baby. My sense is, that because he left under the conditions I've described, he has vacated his rights. Is that an incorrect assumption? I would greatly appreciate any insights!

[annjd]

File for divorce and the US courts will most likely set custody and visitation basically as you want it--especially given his behavior etc.
--he certainly will not get full custody.

I am starting that process. I guess I'm very worried about any visitation in light of what I believe to be a fairly high risk the baby would be taken from the country. Anyway, thank you for responding. You've given me at least a glimmer of hope.

[able1]

If that risk xists then let the judge know and he will take precautions. It is hard to travel these days with just an infant and one parent--often the parent is stopped at the border without docs showing it is all legal and okay.