Well, technically speaking, Nicholas could not legally abdicate for Alexei (so far as I know), so legally, at the time of his death, Alexei would have been the Tsar-pretender. If i am wrong about this, please correct me. Like I say, I am pretty sure the Nicholas could only legally abdicate for himself, and if this is the case, then no matter that he then said GD Michael should be Tsar, Alexei was in fact the Emperor of Russia.