After reading The Real Barenziah (Un-censored, Heh) & finding out she was a "Pro...Pro...prosttute" (Not really, but she was a skank), the part about her being pregnant with Tharns babe piqued my interest. It's mentioned Dunmer can only have up to a max of 4 kids & even then that's virtually impossibly-rare (I get that Tiber being special helped him knock her up & Her love for Symmachus [SIC] resulted in Helseth & Morgiah). Plus due to him being of a mix of races, the chances of him knocking her up cut the impregnation possibility even further. With of all these 'facts' I'm left with alot of questions I'm hoping someone here more knowledgeable than i can answer:

What happened to the kid?
Did she really birth it or just have it aborted?
Did Helseth maybe kill it?
Is the baby's existence even Canon or was it Retconned?

Any help answering these would be great.
Cheers
Val :poke:

We don't know what happened, she gave birth to the child and it is alive because that is the only interesting option, I can't see Helseth being competent enough to outwit his mother, and the existence is open ended. Since elves live a long time, this offspring could show up in any future Elder Scrolls game, but most likely won't.

If he is still alive,does this mean he would have a claim to the natural disastathon and argonian invaded Morrowind and Wayrest?

Do you mean "could he claim the throne of Morrowind and Wayrest?" I suppose he could try, but I doubt that a bastard child of the most evil man in Tamriel would be accepted as king, even if he somehow managed to prove that he is Barenziah's. Theres almost no chance he could ever hold Wayrest, since Barenziah was only a second wife to its king, who himself had plenty of offspring to continue the line.