Well you didn't include my favorite empire - the Ottomans - so I settled for the Mongols. The Mongols have always intrigued me due to their contagious diffusion over the span of three generations. From the time of the unification of the various Turkic and Mongol tribes to the grandchildren of Genghis Khan, the Mongols made the largest empire in human history. Check out this map.
The color changes are a result in a rift in the empire caused by the division of the empire. See, the Mongols weren't sure which of Genghis Khan's grandchildren to follow, so they divided it up. I unfortunately don't have the key, but you understand the sheer size of the empire. Rome nor Britain ever accomplished this, let alone as quickly. I will provide the comparison maps in spoiler tags.
While the size of Britain and the Mongol Empires may seem close, you have to understand the distorted size of the land masses to created the accurate shapes and ocean/pole sizes.
You can also thank the Mongols for rice in China.
Mongols overall were an awesome empire. They weren't intellectuals, but damn did they know how to fight.