Antarctic Bottom Water is the most voluminous water mass of the World Ocean, and it feeds the deepest and slowest component of ocean circulation. The processes that govern its lifecycle are therefore key to the ocean's carbon and heat storage capacity on centennial to multi-millennial timescales. Here, we explore how and where Antarctic Bottom Water upwells across density surfaces in the abyssal ocean. Using an observational estimate of the global ocean thermohaline structure and diagnostics based on the density budget of deep waters, we examine the roles of basin geometry, geothermal heating and mixing by breaking internal waves for the abyssal circulation. We show that the shape of ocean basins largely controls the structure of abyssal upwelling. Mixing powered by breaking internal waves is estimated to drive only a small fraction of the maximum Antarctic Bottom Water upwelling rate. Geothermal heating plays an important role for the upwelling of waters covering large seafloor areas. The results call for alternate sources of mixing along abyssal boundaries, and for the inclusion of basin geometry in conceptual models of the meridional overturning circulation.