According to starwars.com, Tarkin was the guy put in charge of the Death Star. In charge of overseeing it's building, and then running it once it was completed. The Emperor hardly ever left Corusant, and Vader was his Sith representative. Tarkin was acting head of the Imperial Army (and a damn good one, I might add...damn, I have such a soft spot for the Imperium...). If you do a bit of digging, apparantly, Colonel Wulf Yuaren (guy with the mustache in the background during the whole scene where Motti gets choked. Apparantly, he was an intelligence officer assigned to make sure Tarkin stayed loyal to the Empire.

And as for Vader being on Tarkin's lease...

I think the Emperor was in charge of both of them. Tarkin was the brains, and Vader the brawn. Together, they were at the top of the Imperial Army. Plus, I think they've known eachother a long time, and had a mutual respect for one another. They seem almost chummy together, even tho Tarkin is technically above Vader. They seemed to work together and almost be like a team. It was cool.

Anyway, just my thoughts...