In the States, "I've gotten" would normally be used for the continuing meaning ("I've gotten a bit heavier
lately"), but the possession meaning would be expressed without "got", simply as "I have a list" or "I don't
have a list".

US'ns also use the possessive form "I've got," which brings us full circle on this thread, as it's used in "I gotta go."

Gotta go,

Hyla

p.s. Was tickled to notice that Ænigma reads gotta as gotten - maybe it's paying more attention than I thought.