Rey's Falcon when did she gain ownership?

I mean, Rey had just stolen the ship fair and square, so for the big chase scene, you could say it's hers fair enough for a couple scenes. It's nothing to get worked up on. And it's not that they're ignoring canon.

Assuming Han legally owned the Falcon, didn't leave a will, and was divorced from Leia then Kylo would be next of kin and the Falcon would be his ship by the end of the movie, but while it may be technically correct to call it Kylo's Falcon, that's weird and confusing and fails to communicate anything, and legal ownership of the Falcon is super sketchy anyways since it was probably stolen more times than it was bought and is probably thoroughly undocumented.

So, Rey's piloting it for the snapshot they take it from? It's hers at the moment, within a reasonable margin of error.