Apparently it's not only American. I'm Australian and I use it. Until a few days ago, when someone at work pointed it out to me, I had no idea it should be "have" and not "of". I still find it weird to use "have" in some contexts, such as "would have had"; it sounds a bit redundant. In my mind it should be "would of had". I guess old habits die hard; 30+ years of using "would of/could of/should of" took it's toll on me. The weird part is, I tend to say "You shouldn't of have" when I mean "You shouldn't have", because the "have" part is new, and the "of" part is always there for me... LOL. Leaving it out would feel like something is missing.