I think it's when they intermarry. My grandparents were identified as Irish, French, and German (although we suspect other elements were also present). My parents were half-half, and my generation of the family was quartered. My parents didn't claim any ethnic identity, but would say they were half and half. My children have very little idea of their ethnic heritage, and claim to be "Californian" (although my firstborn was born in Berlin).

Now, my wife was the product of Polish-American parents and Polish-born grandparents - she she claims she's Polish.

On St. Patrick's Day, I'm Irish - even though only one Grandmother was actually Irish. Most of the rest of the time, I claim to be German.

-Joe-