Very large. World wide governments were impossible until modern transportation and communication. So if you want to find the limits of your empire find the limits of modern travel and communication.
The British were able to hold on to empire that was separated by months of sea travel. So take that as your limit but changes sea travel to air travel.
An airplane can cross the world in a few hours, obviously an empire that so big that it would take months to cross it by air would be several times larger than the Earth.
Of course governing an empire that large would be a super pain, but not impossible. Most likely the empire would be separated into large, mostly self-governing states, all loyal to a central government.
