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I haven't been able to find a straight answer on this anywhere. I have dual US/German citizenship. I know that I have to enter and exit the US on the US passport and the EU on the German one. But where exactly do I "exit" the United States? There is no passport control for departures in the United States. And based on what I've read, airlines send your check-in information to your destination. So when flying to Italy, I'd have to scan my German passport at airline check-in because I'd be using that one to enter Europe. Is that correct? How do other dual US/EU citizens deal with this? I want to be sure I do it the right way on an upcoming trip. It's been years since I've flown internationally, so there was always a person I could show both to at check-in, but I've heard from friends that now it's all just kiosks and that the people at the counters don't check you in - they just direct you back to the kiosks.
Edit: The thing that's confusing me about previous threads on the topic is that many, including the one someone said my question is a duplicate of, say to show both at check-in in the United States. Kiosks only allow you to show one, so which one?