As far as t-rex's go, I am partial to the premise that it was not in fact a predator, but instead a scavenger. It large sinus caveties are paralleled in the vulture due to the need for relying on smell to track down carcases to scavenge. Also their tiny arms and large legs would not make it practical to function as something prone to running after food, because the chance for tripping and falling and breaking a linb would be too high. Though if he were covered in feathers, I think that would set up a whole new series of nightmares about 12 ft tall pidgeons...yyeeessshhh