It used to air on Cartoon Network a long time ago. They showed all of it back then, except for the new stuff that has come out in the recent years. I've seen most of it. I have seen all three OVAs, Tenchi Universe, and most of Tenchi in Tokyo (but it is pretty poor). I have seen all three movies, but the first one is only good one. I own the Mioshi Special and Pretty Sammi OVA, never aired. I have not seen Project S or the other Sammy related show and I have only seen the first episode of Techni Muyo GXP. But GXP introduces new characters that appear in the third OVA.
There is apparently a few different authors or creative minds behind the Tenchi stories. The original man behind it did the OVAs, the first two. Tenchi Universe is a retelling of the OVAs from a second author's view adding in Kiyone. I don't remember but I think GXP is another person and they did the third OVA as well. But it is not strictly done by the original author, since it brings in new characters that were not part of the story before. It does bring conclusion to the 3 Goddesses and Tenchi though.
There is also a special that goes along with the third OVA, but I haven't found it. It explains a few more things.
But Kain and Kagato were the best villains, though I am a little more fond of Kain. He was a really cool villain. Kagato was definitely a good villain, but Tenchi Muyo in Love, well its a movie so it just looks better. The amount of effort that they had to go through just to kill Kain, makes him a superior villain. And turning into Godzilla, can't beat that.
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