For more than five decades, the Mediterranean Sea has been identified as a region of so‐called thermohaline circulation, namely, of basin‐scale overturning driven by surface heat and freshwater exchanges. The commonly accepted view is that of an interaction of zonal and meridional conveyor belts that sink at intermediate or deep convection sites. However, the connection between convection and sinking in the overturning circulation remains unclear. Here we use a multidecadal eddy‐permitting numerical simulation and glider transport measurements to diagnose the location and physical drivers of this sinking. We find that most of the net sinking occurs within 50 km of the boundary, away from open sea convection sites. Vorticity dynamics provides the physical rationale for this sinking near topography: only dissipation at the boundary is able to balance the vortex stretching induced by any net sinking, which is hence prevented in the open ocean. These findings corroborate previous idealized studies and conceptually replace the historical offshore conveyor belts by boundary sinking rings. They challenge the respective roles of convection and sinking in shaping the oceanic overturning circulation and confirm the key role of boundary currents in ventilating the interior ocean.