Hi here's a bit of what I know, in extremely condensed form
Michael Gray claims that he is the illegitimate son of Alexei, so obviously Alexei is supposed to have survived, according to Gray. Er he also states that his mother was Princess Marina, Duchess of Kent, Prince Michael of Kent's mother!!, though of course he was adopted by a family in Ireland, and forgotten.
Plus much more too...
It really sounds like he is a loony, doesn't it, but the strange thing is his story afforded a article in the British newspaper 'The Guardian' a broadsheet, with a good reputation unlikely to use purely sensational stuff.
Of course nothing has come of all this, but its quite a good read all the same, if that is you already know something about the Romanovs beforehand.
Katie