I noticed that a LOT of people never mention the fact of Tenchi's race....isnt he part jurian as well as part Airian because of Airi?...apparently no special genectic abilities are given to the airian species...

Mostly it's the other way round, that they don't mention he's part Airi-jin as well as Jurai-jin.

Of course, this assumes they're all different species rather than nations.

His grandmother, Airi Masaki (formerly Magma) is from the Airai nation. It's supposedly the second biggest nation in the galaxy (after Jurai), although the TTN - Yosho describes it as a religion. Then of course there's the Seniwa space (where Mihoshi comes from), The Renza Federation, Balta Space, the various Galaxy Union planets and areas, and probably some other small unaligned worlds.

This is one of the reasons why I like Tenchi Universe more then the OVAs, no crazy family tree.
In TU, Tenchi's part Earthling, part Jurain.

Yeah but sometimes the complexity's half the fun. Besides, I don't have to think that hard, usually Jibri's around to crunch the numbers and spit out refined data.

Assuming of course that his dna splits up into such neat little fractions. And that there's nothing else mixed in with that.

Yeah, you're only guaranteed 50% of each of your parents DNA. Beyond that, what comes from ancestors is just calculated on what will go through on average. That's why full siblings can share with each other absolutely nothing genetically except their mother's RNA, or be 100% identical (either as twins or born seperately), but on average will be about 50% identical with each other.

I don't think Tenchi's race has much to do with anything. Kami Tenchi sought his place in the universe, and being Nobuyuki and Kiyone's son was it in terms of time and place. Much like how most of Sasami's special powers will have nothing to do with Azusa or Misaki genetically, just her connection to Tsunami.