From their roots in South America, the dinosaurs migrated "in a frenzy of movement to cover the planet".
Hundreds of different dinosaurs appeared, from the ferocious T rex to the gigantic long-necked Diplodocus.
However, by the time the asteroid struck, killing them off, they were starting to decline, as they had ran out of space on Earth.
The research published in the journal Nature Ecology and Evolution, reconstructs the paths taken by the dinosaurs as they moved out of South America.
The dinosaurs were able to take advantage of a "blank canvas" left by the extinction known as the Great Dying, just before they appeared, Venditti was quoted as saying by 'BBC News'.
They quickly spread across the devastated planet, taking up every opportunity to expand, with little competition for food, space or resources from other animals.
Soon their progress slowed, as they became adapted to almost every habitat on Earth. Only avian dinosaurs survived to become the birds we know today, researchers said.
"It would have been the final nail in the coffin for them apart from the birds," O'Donovan said.
The research is based on a statistical method that mapped where every dinosaur and its ancestors existed on the globe.
This gives a more complete picture than studying fossil evidence alone, which is patchy and incomplete, researchers said.
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