I suppose at the point where one feels closer to the "generic" American values/culture than to that of your forebears. I think it's the truest definition, however it is often hard to prove/demonstrate, so the arbitrary definition "have be born in this country" is used instead.
so the arbitrary definition "have be born in this country" is used instead
That hardly seems arbitrary -- it's what the word means. If you were born outside the country then you have immigrated, therefore you are an immigrant.
Well it may seem a bit arbitrary to those who grew up in the U.S. but were born elsewhere (or even to those who were born in the U.S. but grew up culturally isolated).
