"Vielen dank" to Dr Einholm for holding down the fort here, I'm glad the regulars are not the only academics who are prepared to challenge and refute the ridiculous Pangea hypothesis. Welcome to the fold, doctor.
And, yes, you can see how (just as an example) several species of bipedal carnivores, all similar to the Tyrannosaurus Rex, appear in every continent, with the possible exception of Antarctica. By comparing the different anatomical differences and dating of strata where the fossils were found we can see how they all came from common ancestors. But of course, you know this since you work in Evolutionary studies and therefore have read extensively about the subject. Or... have you?
The word you're looking for is "theropod", but you're excused - it is unreasonable to expect scientific laypersons to employ the correct nomenclature all of the time. Now, I know for a fact that most species of theropod were confined to very specific geographical areas, consistent with seperated continents and some sea-travel. Tyrannosauroidea, one clade of theropods (those most similar to the Tyrannosaurus - perhaps you specifically meant these?) were confined to North America and East Asia, much like the Dromaeosauridae (the family which we have already examined in this thread).
Your refusal to use proper terminology makes it difficult to ascertain exactly what you are trying to say, but it seems you think that either the Tyrannosauridae specifically were ubiquitous (they were not), or that some other family of theropod was (I cannot think of one with the worldwide coverage you're suggesting).
Now, if you'd like to point me to a specific species of theropod which has the ubiquity you claim it to have, I will gladly examine the evidence surrounding it. As it stands, you seem to be rather out of your depth. You ought to do some serious reading on the fossil distributions of theropods before you go making wild unsubstantiated claims about them.