The OALD has the following note about get:
In spoken North American English the past participle got•ten /ˈɡɒtn/ /ˈɡɑːtn/ is almost always used.
I know that I have got a car just means I have a car. Excluding that case, do Canadians and Americans really use gotten as past participle when speaking? Does that mean they use got as past participle when writing, but gotten when speaking?
Notice that the OALD reports got as past tense, and past participle of get. This, and the sentence I previously shown makes me assume the dictionary is saying that gotten is used in spoken English from Canadians and Americans, while got is used from Canadians and Americans when writing.
I remember that an American friend of mine (born and raised in the East coast) told me I should write have got, not have gotten.