Babylon-Egypt-Greece-Carthage-Rome-Franks-Holy Roman Empire-Byzantine-Venice-Spain-France-Britain-Germany-America
As the old historian once said, the Holy Roman Empire was neither Holy, Roman, nor an empire. Putting it up there is a tad silly. And the Franks' claim to fame is stalling the Muslim conquest of Europe and uniting a few lands there, granting a VERY temporary, minor renaissance. No sooner did they splinter than the Viking's started pillaging at will throughout Europe.
After Rome it'd probably look more like this: China, China, China, China, China, China, Napoleon's Empire, British Empire, Germany, America. (India was very rarely a united entity during that period of history, so hard to list them above China. Maybe a brief period under the Mughals)
If we remove China from the equation, it might go like this.
Rome, Eastern Roman Empire, Umayyad Caliphate (furthest extent of initial Muslim Conquest).
After that its a tough call until the Mongol Conquest. Europe was a splintered backwater, so its hard to mention them. The Byzantines were still strong, but the initial Mongol expansion pushed them back hard. India was still divided. Probably the Seljuk Turks' empire, but that didn't expand til later. So we're left with a few hundred year gap here. Probably put it between the Eastern Romans and one of the Caliphate successor states.
Than the Mongol empire. Without question. Even if we exclude China, they pretty much controlled everything East of Poland.
After that there's no clear successor without China in the mix. Venice made its rise around this time. Than eventually the Ottoman's became dominant. Mughal's were huge as well a bit later. Around that time Spain was making its own global play. For a couple of centuries you could probably pick one of those three.
Than Napoleon conquered most of Europe and made a brief blip for the top spot, Britain had probably surpassed Spain and everyone else even before that and most certainly were tops after that. And the rest is already covered.
