Bottom line is that whilst there's a lot of whining about it being an Americanism it is, in fact, more grammatically correct than the crap most English people come out with - it's the correct past participle of get.[/QUOTE]
Well it's a past participle of get" as is "got". Although t's perhaps relevant to note that in most North American dialects there are situations where "have Got " is the form used
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 contexts as
•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 allow
•*I've gotten the answer.
•*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)
from
http://english.stackexchange.com/questions/5531/difference-between-i-have-got-and-i-have-gotten
•They've gotten to leave (they've managed to leave).
As to grammatical correctness you have a reactionary
prescriptive approach to language. You need come to terms with descriptive linguistics and the whole gamut of kinky dialects and idiolects that are out there.