I heard it splintered, but if it did how does the Empire still exist?

Any help lore buffs?

I think it's more Tamriel that has splintered/is in the process of splintering and the Empire still exists in Cyrodiil and are just trying to maintain as much control as possible.

Unfortunately I don't think there's much lore from the time of Skyrim since the game hasn't come out yet, so we'll probably just have to wait and see to know for sure.

by the time of the infernal city: the empire had fallen, the new emperor only holds part of cyrodil (some of which is tenuous at best.) however, iirc, infernal city is approx 40 years after oblivion. skyrim is based 200 years after oblivion - so, in that time, the empire could be back to being a strong power fairly easily.