There are Australian fossils just over 100 million years old that do seem to be from a small, advanced tyrannosauroid, close to Xiongguanlong and Tyrannosauridae. Timimus may be a member of the same genus (femur length just over half that of Albertosaurus, 2/3rds of Gorgosaurus).
Recently, it's also been proposed that the megaraptors are tyrannosauroids rather than allosauroids, and several of these are known from Argentina and Australia.
Aside from the megaraptors, I don't know of any tyrannosaur finds in South America. However, Antarctica served as a joining point between Australia and Patagonia at various points over the Mesozoic, apparently right up to at least 72 Ma, so there was a chance for fauna distributing between them.
As for Tyrannosauridae, China also had Zhuchengtyrannus, Alioramus and Qianzhousaurus along with Tarbosaurus. It does look like the group evolved in western North America (Laramidia), probably crossing to Asia through the Bering land bridge near the end of the Cretaceous.
No finds in Europe or eastern North America (Appalachia) yet. I don't think they ever got to the latter, more basal tyrannosauroids filled the apex predator niches there right up to 67 Ma.
