When it comes to animals they are considered property however in most state their are specific laws when it comes to animal abandonment, care etc
To prove abandonment you need to report the animal(s) as being abandoned to animal control, after a certain amount of time (pretty short) if the owner (ex-girlfriend) does not claim her animals you will be able to legally take ownership if that is what you want.
Without paper trail or proof you will just take care of them for free until she decides to get them as they will remain her property.
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