Name of dominant dinosaur
The closest example I can think of is Lystrosaurus, which was one of the most common animals in the early Triassic period. It was distributed across many modern continents, and was roughly the size of a pig or cow, depending on the species. Lystrosaurus was not a dinosaur, despite its name. 



Excerpt from the Wikipedia page (emphasis mine):


  Lystrosaurus is notable for dominating southern Pangaea during the Early Triassic for millions of years. At least one unidentified species of this genus survived the end-Permian mass extinction and, in the absence of predators and of herbivorous competitors, went on to thrive and re-radiate into a number of species within the genus, becoming the most common group of terrestrial vertebrates during the Early Triassic; for a while 95% of land vertebrates were Lystrosaurus. This is the only time that a single species or genus of land animal dominated the Earth to such a degree