Do illegal aliens have parental rights?

My friend, Cindy (US citizen), got pregnant with an illegal immigrants baby. She doesnt love him (spare me the criticisms), but she does want the baby to know his father. But they live three hours apart from each other. Omar (the dad) says he loves her and is getting creepy about it, saying he will get a lawyer and "do whats best for the baby." Can he go to court to get custody? Or partial custody? Or will he get in trouble for entering the country illegally? Also, if they live three hours apart, how does partial custody work?

He lives in an apartment with another single immigrant. They smoke and drink and I dont think if this is a great enviroment for a child to be in.

Answer:
If as you suggest the other is here illegally, my suggestion - call I.C.E.
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