In the video Two-and-a-half billion T. rex roamed Earth, study finds contains a short explanation of the results in Science Absolute abundance and preservation rate of Tyrannosaurus rex by the corresponding author of the paper.
I'd like to understand better what is known about T. rex's adaptability and range of environments where it was thought to flourish. It's hard to imagine what things were like back then, so using modern flora/fauna and climate distributions as reference points will help me to understand this better.
Based on that knowledge and reference frame, I'd like to ask about the following Gedankenexperiment:
Question: Would anything limit an "invasive species" T. rex introduction now besides running out of food or intervention by humans?
Would they basically thrive over much of the Earth's surface and eat all the other mammals? Or without a supply of dead and rotting dinosaur cadavers would these giant scavengers with excellent olfaction quickly deplete a small region and die of starvation?
Currently there is not likely enough DNA to reconstruct a full genome nor a scheme to build and incubate a dinosaur egg for it (as far as I know), so we are not at any risk of this happening in the near future.