A few thoughts...
- Harry was so terribly attached to his friends at Hogwarts because they were the only friends he'd had. In this world, that would attach to the Tenchi Muyo gang. He'll still have friends at Hogwarts, but he probably won't cleave to them quite as hard. He'll *also* likely be used to the idea that the Tenchi gang regularly deals with major supernatural threats of various sorts, which will mean that he's going to be hitting home for whatever fire support is available when disturbing things go down.
- So, he goes into the lab. Check. He comes back out in a house full of people who treat him well, and have a habit of taking in strays. Check. Why would he ever go back to the Dursleys? Why would the Tenchi cast let him? I mean, you might chalk it up to failure to communicate for maybe a trip or two, but pretty quickly, he's going to come to the point where he doesn't want to go back, and there's absolutely nothing that will force him to. (...except possibly for Dumbledore, and wouldn't it be interesting to see how *that* interaction turns out?)
- Harry was so terribly attached to his friends at Hogwarts because they were the only friends he'd had. In this world, that would attach to the Tenchi Muyo gang. He'll still have friends at Hogwarts, but he probably won't cleave to them quite as hard. He'll *also* likely be used to the idea that the Tenchi gang regularly deals with major supernatural threats of various sorts, which will mean that he's going to be hitting home for whatever fire support is available when disturbing things go down.
- So, he goes into the lab. Check. He comes back out in a house full of people who treat him well, and have a habit of taking in strays. Check. Why would he ever go back to the Dursleys? Why would the Tenchi cast let him? I mean, you might chalk it up to failure to communicate for maybe a trip or two, but pretty quickly, he's going to come to the point where he doesn't want to go back, and there's absolutely nothing that will force him to. (...except possibly for Dumbledore, and wouldn't it be interesting to see how *that* interaction turns out?)