Past diaries found here--
The beast has dwelled within museum halls and captured the minds and imaginations of the people for over a hundred years--Tyrannosaurus (Tyrant Lizard).
It lived in the late Cretaceous, one of the last theropods to occupy the northern hemisphere (part of a group called the Tyrannosauridae that took over the massive meat eater niche in the mid Cretaceous, though Tyrannosaurus itself did not appear readily until much later--roughly 68 million years ago until non-avian dinsoaurs were obliterated 65 million years ago).
Absolutely, I'd be running.
Well... there are those who disagree. This guy for example--
Jack Horner of the Museum of the Rockies, one of the primary influences for Michael Crichton's character Alan Grant--possibly most famous for his work on dinosaur nesting behavior and the probability of the herbivores moving in herds (I'm convinced some if not many theropods lived in groups as well, but that's another story).
There are several lines of evidence he points towards.
First was its arms.
First of all, it had two fingers (as opposed to the dinosaur and, not surprisingly--bird tri-finger characteristic), not quite so useful for grasping fleeing prey.
But even more important was its scale--relative to the creature itself, they were barely evident. Their functionality was quite obviously less important than it was for many other large theropods (who do indeed also have small arms, but nowhere near the extreme that Tyrannosaurus takes it).
Secondly he points out the shape of its teeth--most predatory dinosaur teeth are blade-shaped and laterally compressed with serrations (thin and sharp!). Sorta like this guy--
Tyrannosaurus on the other hand held teeth that were designed for crushing bone, not slicing through meat. He argued that teeth like this would be ideal for a scavenger trying to get as much from its meal as it could (bone marrow can be quite nutritious), but not so useful for a predator slicing chunks of meat from its prey. Its jaw was also designed for this bone-crushing functionality with one of the strongest bite forces known.
He also points out its highly developed olfactory cavity--it had an amazingly well-developed sense of smell, superb for a scavenger searching for a carcass.
But most are not convinced.
Beyond ecosystem reconstruction (assuming we have a good sample of large theropods of the era and that there wasn't an entire different genus that we are not aware of), one of the most telling lines of evidence was given by Ken Carpenter.
A portion of a series of this hadrosaur's caudal (tail) vertebrae were bitten off by a Tyrannosaurus in life--they were then given the time to heal, implying that it not dead when the Tyrannosaur chomped down.
This shows that at least sometimes Tyrannosaurus would attack live prey.
My thoughts are somewhat of a midline--like most modern predators, I have no doubt it would have scavenged any chance it could get; a corpse is much easier to deal with than a creature interested in its own self-preservation. However, I also think that if the opportunity arose it would gladly attack the Late Cretaceous wildlife for a meal--the teeth do suggest a differential methodology of feeding (my own thought lies something like the African lion but without arms to hold the prey--take the bone crushing teeth and clamp down on the bone to sever the spinal chord or throat). It wouldn't slice repeatedly with its teeth--they weren't designed for that.
Granted, this's mostly just speculation on my part, but it seems to match the evidence at hand.