Originally Posted by
FlyingScientist
How would I currently travel e.g. between the US and Canada if ETA for Canada is registered on a passport other than the one I entered the US with? How will the US authorities know that I left and the Canadian authorities know that I will be coming (and the airline see that I am authorised to do so)?
You can enter/exit the US on different passports, they match the exits and entries by NAME/DOB/entry biometrics etc. not by the passport number. The correct record even shows up online.