I agree with Bingly here. "Have got" should imply possession or receipt. People often say, for example, "I've got a cold," but, grammatically speaking, they'd be more correct to say "I have a cold."
In a slightly different context, one might say, for example, "I was with my ailing nephew, and now I've gotten a cold." Note, however that one would use "gotten" here, instead of got.
Similarly, I think, one might say, "I got it in the mail," to express receipt of a letter; but one could say, "I have gotten it in the mail," to imply that the letter is now in possession of the lettercarrier.
Occasionally, I think, it's fairly common usage to use have got for emphasis, as in: "You have GOT to be kidding!"
The 'have got' construction has been around forever. I remember the old TV program I've Got A Secret. When we were learning our grammar, way back then, I called this to my teacher's attention and, though she was a pretty strict grammarian herself, she admitted that this had escaped her notice, gave me extra points for my vigilance.
Interestingly enough, the show was sponsored by a cigarette company (yes, I'm that old), whose catch-phrase was "Winston tastes good, like a cigarette should". This, of course, should be: ...as a cigarette should.
But I digress.
Ron.
