Kicking Him to the curb, Sueing her for custody

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A friend of mine has been dating this man for about 3 years. They have a daughter and live together. This past weekend, she found out that he had been cheating on her. So she packed all of his things and moved him out. They had a big blow up where he accused her of not having enough time for him because she spent all her time at her new job or with their baby. She told him that he resented her for not being dependent on him anymore. Then she found out that he had been seeing the other girl for over a year and this other girl was some woman who had be purposely antagonizing my friend at bars and clubs. My friend just thought that this other girl was some troublemaker who she just happened to be running into constantly. Turns out that these run-ins were not coincidence and the other girl has been laughing at her to my friend's boyfriend. He knew all about it. Now that all of this is out in the open, the guy has left their apartment and is looking for lawyers so he can sue for custody of their daughter. I wonder on what grounds. Does he have a case?