My husband has been deported does that mean I have sole custody of my children?

Hello a:

Not legally - but in practice.. If he EVER gets back, he'll have equal rights to his kids just like you have.

I'd STILL memorialize the split and/or deportation in family court. He'll be ordered to pay child support even in a foreign country.

excon

I am not sure but I would file papers with the court system to protect yourself.

No, it merely means he is now living in another country

You said husband, ( not ex) so are you planning on moving to where he is, or trying to get him back to the US.

But if you want sole custody, you will have to file for divorce or legal separation and then file for custody of the child.