This below comes via Google......
Here's what David Crystal says about The gotten/got distinction in
The Cambridge Encyclopedia of the English Language (p.311):
"Gotten is probably the most distinctive of all the AmE/BrE grammatical
differences, but British people who try to use it often get it wrong.
It is not simply an alternative for have got. Gotten is used in such
They've gotten a new boat. (= obtain)
They've gotten interested. (= become)
He's gotten off the chair. (= moved)
But it is not used in the sense of possession (= have). AmE does not
*I've gotten the answer.
or *I've gotten plenty.
but uses I've got as in informal BrE. The availability of gotten
does however mean that AmE can make such distinctions as the following:
They've got to leave (they must leave) vs
They've gotten to leave (they've managed to leave)."
I'd add that Crystal's I've gotten the answer isn't starred if it means I have figured out the answer, rather than I have the answer.
The key is the overlap between the Possessive use of have and the Perfect use of have, plus the fact that one of the senses of get is come to have. If one has come to have a cold, for instance, then one has a cold, and the AmE usage of has got means that one is currently infested, due to the present relevance aspect of the Perfect. This is so common that kids regularly use got without have or even -'ve to mean have, and young kids even think it's the regular verb for possession, as witness such constructions as He gots new shoes.
Faced with the overwhelming interpretation of (ha)ve got as simply have, AmE has innovated a new past participle gotten to be used whenever other, non-possessive forms of get are intended.
If one is simply speaking of the acquisition of something, for instance, rather than the current possession, one says I've gotten ..... in AmE since I've got implies that one still has it, and therefore focusses on the current Possession rather than the Perfective acquisition. And all of the idiomatic uses of get, like the get-Passive of get married, the Inchoative become/come to be inherent in get tired, the Concessive of get to go that Crystal mentions, etc. use gotten as their participle. Whereas any construction, even an idiomatic one like have to (= must) where one can use have equally well, use got as the participle.
Weird, but that's English for you.
"Bipolar is a roller-coaster ride without a seat belt. One day you're flying with the fireworks; for the next month you're being scraped off the trolley" I said that.