Surface currents are greatly effected by the winds and through forces described as the Coriolis effect, will move in a clockwise direction to the north of the equator and counter-clockwise to the south.
Deep currents are driven primarily by density differences (created by temperature and salinity), and so the salty cold water from the poles will travel along the deepest parts of the ocean basin. If the ocean floor is flat enough, I believe the main current would tend toward the coast with a surface current traveling in the same direction, but depth will be the primary factor.
Starting at the points water sinks.
On Earth, there are two primary locations that water sinks on a large scale, and the mechanics of each are similar, but have differences.
In the North Atlantic, cold winds blow across the surface causing evaporation. This has the dual effect of cooling the water (increasing density) and increasing salinity (only pure water evaporates; increasing density). This denser water sinks and flows southward. The equatorial region of the Atlantic is a relatively small region and there is little upwelling there. The northward flowing surface current is still less dense than the deeper current. Most of this current ends up in the Southern Ocean, where it splits; part going to the Indian Ocean and the rest flowing past Australia into the South Pacific.
In the Southern Ocean, cold winds blow out from Antarctica. This wind breaks up the ice and blows it north leaving the ocean surface bare to this freezing wind. The surface quickly freezes, with purer water forming ice around pockets of brine. This brine lowers the freezing point, which allows it to "melt" its way through the ice, dropping free and its density causing it to sink to the bottom. This briny water is denser than that coming from the Atlantic and it flows out to the Pacific.
The Equatorial Pacific is a huge area, all warming; expanding and becoming less dense. The outflow from the Atlantic causes its surface to be slightly lower than that of the Pacific, which means this less dense water flows ever so slowly through Indionesia, the Indian Ocean and into the Atlantic, where it joins the surface flow to the North Atlantic.
If the Ocean Basins were separate basins instead of essentially a single "world ocean", this conveyor system would not work. This is obviously true if the basins were completely divided, but even if connected through shallow archipelagos or over continental edges, without a continuous "ocean deep", the circulation would be limited to individual basins. And if each basin was not both large enough and did not stretch far enough between pole and equator, such local currents would be limited even further.