Name: Ayeka Masaki Jurai
Occupation: Crown Princess of Planet Jurai
ORIGINS
Ayeka's origins are pretty much the same in all of the principle three mainstream canons - although her exact connections to the Jurai throne are tweaked with a bit over the course of each series.
In the OVA, Ayeka is the daughter of the Emperor and his wife Misaki - but then, the Emperor has more than one wife, and it's quite possible he has more than the two he brings along with him to the planet Earth. Ayeka's mother is referred to as the 'Queen of Jurai', which suggests she is his principle wife - however, Azusa's other (Earthborn) wife Funaho seems to be of equal status, the mother of Ayeka's half brother (and fiance) Yosho.
There is a big age gap between Ayeka and Yosho, and she knew that from a very early age she was supposed to marry him, although when he left to fight Ryoko and defeat her, she was still growing up. Her arrival on the Earth is in search of Yosho and his tree, Funaho, which brings her into the whole Tenchi setup. She is also the older sister of Sasami - a role she plays in all the series, and one which is spoofed upon a little at the end of the Pretty Sammy series, when Romio claims Sasami was her baby sister.
Ayeka's lineage is more foggy in the Universe and the Tokyo series. We're told in Universe that the throne of Jurai is vacant 'pending marriage of the Princess Ayeka' and that she is only a member of one of many branch families. However, she is also cited as first in line to the throne, and when we first encounter her, she is embarking on marriage meetings, presumably because she has come of age and must choose a husband to settle Jurai's future. (Her reluctance to do so can inadvertantly be seen as the cause of Kagato's rise to power!). However, in the Tenchi Muyo In Love film, the Galaxy Police Detective tells Ryoko that the 'current emperor' has nothing to do with Kain, so somewhere between Universe and the film, an Emperor has been invented...making it really hard to work out what's going on exactly with Jurai!
In Tenchi in Tokyo, they don't even bother trying to explain her lineage. She comes into the series simply pursuing Ryoko and Washu who have stolen something precious to Jurai, and she is the Crown Princess of the planet (who apparently throws away all claims to Juraian responsiblity to live on the Earth and abandon her planet to who knows what fate!). Her parentage and family background is unknown, although it is presumed that she is a descendant of the Empress that confined Yugi and banished her to space.
The implication in the Universe series is that Ayeka cannot be Queen of Jurai without a husband and all the other shown claimants to the throne are male. This suggests that salic law is prevalent on Jurai (anyone not familiar with history or those things, salic law is the law which entitles only men to inherit the throne, and quite often historically women could only pass their line through marriage and children if there are no male candidates available). In the OVA, Yosho tells Ayeka he left because there would have been conflict between them for the throne, indicating that either or both of them could have inherited in their own right and probably explaining the reason behind their betrothal. In Tokyo...erm, well, God knows, really ;)