Best way to end a relationship.

I want to end my relationship. Kids are involved. (2). My soon to be ex has cheated since day 1(emotionally) he is constantly txting girls CONSTANTLY or he makes some adultspace page over and over again. Like a dummy I listen when he says "it won't happen again" ( I've been Dumb for 3 years😒) each time I catch him he says He's sorry and he has a "problem" I've tried to forgive him but over the years it's caused a lot of problems in our relationship I don't trust him and I resent him when I think of what he's done. Anyone ever dealt with just finally leaving? Im not mad at him, im mad at myself because I should have left the first time! He told me he had a "problem" right ? Still I stayed and believed things would change😔 they didn't Im so hurt because I give this (excuse me) bitch everything!!!! I just feel so low Im a skinny girl and every time I see him online talking to girls they have these huge butts! That makes me feel like a piece of shit because if he loved me he would see how much this hurts me. I was in labor with his daughter and he was on kik messaging other girls saying he loves them and wants them to have his babies girls he doesn't even know ugh I'm finally fed up because last night I found out he was on a dating sex site😔 why me? I know there are loyal men out there but I'm so afraid to give my all to someone. Im in tears now because so many years have been invested. My kids could be by someone else now I have to introduce someone else into their life. Sorry this is so long and thank you for reading. How did you end a relationship ? Whenever I bring it up we argue! 
Edit** he lives w me! His name isn't on the lease so do I serve a 30 day notice to get him out? Or do I just leave the home?