Educated Guesswork

I'd guess they were largely derived from the greeks and egyptians, at least during the early days. See: http://www.library.ucsb.edu/people/larsgaard/plan1.html for some data (and citations) on the Crates of Mallus globe, which was drawn in four quarters, as well as contemporary map-making. Later Roman maps didn't actually pick up there, though, and are in some ways a throwback to Persian maps, as they used campaign-driven measures (as the Persians used parasangs) rather than attempting a more abstract mapping.

Note that the globes on contemporary coins were largely symbolic of eternity in this period, and would likely not have been representational.

"Blank Space?" Interestingly, at least when I was making maps about 10 years ago, the governments of some countries were still making maps with certain countries missing for political reasons. For instance, I seem to recall viewing a map of Europe and North Africa from the Lybian government (I think -- it may have been another country), with Britain and Northern Ireland missing. It simply showed the North Sea above France. Of course, countries still take all sorts of liberties with borders and place names for political reasons, but simply deleting extant geography is something you don't see very often.

Globes? Wasn't the spherical earth a Renaissance notion?

With that in mind, it's easier to envision a map that elides a lot of what we now know. You can't just leave blank area on a globe.