The TO map is a representation not of the globe, but of the oecumene, ie. the inhabited world (or at least 'our' portion of the inhabitable world). So, it represented simply the connected continental landmasses around the Mediterranean basin (ie. Europe, Africa and Asia) which, for a medieval audience, represented 1/4 of the globe.

Since it was well known that, in the northern hemisphere, it gets colder as you move north and warmer as you move south, the ancient and medieval cosmology viewed the earth as divided into 5 bands from south to north. To the north and south are two frigid bands, too cold for anything to live, and through the middle there is the torrid zone, too warm for anything to live. Here is a good diagram and here is a collection of medieval examples.

Since the Greeks, there as an idea that the earth was harmoniously composed, such that the southern hemisphere should mirror the northern. As such, there was a general idea that there was a southern continent as well. There was some discussion in the ancient world as to whether this continent was inhabited by the antipodes (literally: the opposite, ie. upside down, feet people). Although Christian authors in late antiquity were concerned about the theological implications of there being humans who were unrelated with Adam and Eve, leading many to deny the existence of the antipodes themselves, the continent's existence was itself generally accepted. On this point, there were also sometimes thought to be two landmasses on opposite sides within each of the northern and southern hemisphere respectively, (leading to a total of 4 landmasses cut off from each other by ocean). However, most medieval authors just discuss the two, and so far as I'm aware, no map depicts 4 landmasses.

There are, as a result, some medieval maps that show both the zones and the landmasses, with a T-O map in the northern hempisphere and an amorphous landmass in the south. For example, Lambert of Saint-Omer proves some good examples in his liber floridus (c.1120): 1, 2, 3 (if it doesn't link the right page here, it is folios 69v-70r). Likewise, the aforementioned page of medieval examples of zonal maps has a number with this sort.