I think this has been mentioned before in an earlier thread but to claim that there is only one Nossi Hador is incorrect. In fact, there are none!
The term Nossi was last correctly applied to the last of the Nessi’im in E”Y (I don’t know who that was). Lubavitch – I don’t know which rebbe of theirs it was – decided to adopt the title for themselves, and because no one else believes in this title there is no one who is competing for it!
So lubavitch can safely claim that their rebbe was/is the Nossi Hador… but they are wrong.