The rumors that the OVA will be focusing on the Choushin war (The war between Washu, Tsunami, and Tokimi) is true, and was confirmed a long time ago, but it's worth restating here..
The new information is that they have announced the three main staffmembers behind the show.
Original concept and Supervising Editor: Masaki Kajishima (Also was concept and Editor for Tenchi Muyo OVA 1 and 2, as well as concept, editor, and script writer for Dual: Parallel Trouble Adventure)
Director: Kenichi Yatagai (Also directed some episodes of Tenchi Muyo OVA 2 and the Macross 2 movie)
Script writer: Yosuke Kuroda (Also wrote the scripts for some episodes of Tenchi Muyo OVA 1 and 2, and was script writer for Trigun)
So yeah, look forward to it... they really have some AWESOME people working on the third OVA!
And let me restate one more thing just to keep questions at bay... Tenchi does NOT choose one of the girls in OVA3! This is CONFIRMED! There will be NO CHOICE MADE

However, it is suggested that Tenchi will choose when and if OVA 4 is made. (So yay.. Speculation can still continue
