First off, if you're done, break it off and be done. Get her shit out of your house by this weekend. Pack that shit up and put it in the garage if you have to, but get it gone. Don't give her excuses to keep coming back.
Then, be done with her. Block her on Facebook, delete her number or put it in your phone's blacklist, and don't "date" her or any of that. The only reason she wants that is to keep you hanging around as a fallback in case her new guy doesn't pan out.
Finally, what did y'all fight about and who broke up with whom? It's all fine and dandy to say you're not petty and whatnot, but if she started the fight, and broke up with you over it, it would help to know what it's about to find out what her strategy in keeping you around is.
woodman: achieving the impossible since 1967. 1973? 1980? 1985? 1976? whatever, you get my point
ford's advertising slogan was literally "you can pay for all of it today or you can go fuck yourself"