Carnivorous tyrannosaurs were one of numerous theropod families. Tyrannosaurs arose 170 MYA. The earliest were the size of a modern human.
Tyrannosaurs diversified, but their rise to the top of the food chain was long checked by the dominant allosaurs that arose in the mid-Jurassic and lasted until 93 MYA, in the mid-Cretaceous.
In their prime, allosaurs were almost as large as tyrannosaurs eventually grew to. A mass extinction event, with global warming and sea level fluctuations, laid allosaurs low and allowed tyrannosaurs to take their place.
Tyrannosaurs apparently developed giant body size rapidly, late in the Cretaceous, and their success enabled by their early-evolving keen senses. ~ American paleontologist Stephen Brusatte et al
Tyrannosaurs were fierce predators. They hunted and scavenged and were not above fighting and eating another tyrannosaur.