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Congratulations on that! That's great news, if for no other reason then because you won't be on the hook (score-wise or otherwise) if your ex messes something up.
As far as your score goes, though, it's going to have both positive and negative impacts, and what the cumulative effect will be is really hard to say. A lot of times, people pay off a loan and expect to see a big jump in their score (because, that's what you would think, right?). But they see just the opposite because their mix of credit takes a hit. You may not see that as much as others, though, because you have other installment loans.
My best guess is that it will have a minimal effect on your scores one way or the other (but that's just a guess), but that it will improve your chances for a mortgage, primarily because of the improved dti.
Is it your only installment loan?