Mariah Carey and Nick Cannon separated back in May -- and are living apart ... and we're told divorce lawyers have been negotiating a property settlement and custody agreement for months and the divorce is "a done deal." Sources connected with the couple tell TMZ ... Mariah and Nick have been living in separate houses in NYC since May.  He sees the kids but that's the extent of their contact.Our sources say  ... Nick's appearance on Big Boy's radio show in March was the beginning of the end. Nick played Big Boy's game -- name the 5 celebs you've slept with.  Nick named 5, but our sources say the one that made Mariah insane was Kim Kardashian.  We're told Mariah tore into Nick for weeks ... feeling humiliated and the relationship never recovered.We're told it went from bad to worse when Nick went on Howard Stern and talked about Mariah not giving it up before they got hitched.  She went nuclear.Our sources say Mariah feels Nick has abandoned her by taking every gig that's on the table ... when they don't need the money.  She's especially angry because it keeps him away from their kids.For Nick's part ... we're told he feels Mariah has become impossible because she surrounds herself with "yes men."  He says she can't handle it when he dares to disagree with her.We're also told Nick is incredulous Mariah is bitching about his work ethic ... he says he's generated $75 million since 2011 for the family.