A variety of recent studies have suggested that the meridional overturning circulation (MOC) is at least partially controlled by the Southern Ocean (SO) winds. The paradoxical implication is that a link exists between the global surface buoyancy flux to the ocean (which is needed for the density transformation between surface and deep water) and the SO winds. Although the dependency of buoyancy forcing on local wind is obvious, the global forcings are usually viewed independently with regard to their role as drivers of the global ocean circulation. The present idealized study is focused on understanding this wind–buoyancy connection. In order to isolate and investigate the effect of SO winds on the overturning we have neglected other important key processes such as SO eddies.We present the wind–buoyancy connection in the framework of a single gigantic island that lies between latitude bands free of continents (such as the land mass of the Americas). The unique geometry of a gigantic island on a sphere allows for a clear and insightful examination of the wind–buoyancy connection. This is because it enables us to obtain analytical solutions and it circumvents the need to calculate the torque exerted on zonal sills adjacent to the island tips (e.g. the Bering Strait). The torque calculation is notoriously difficult and is avoided here by the clockwise integration, which goes twice through the western boundary of the island (in opposite directions) eliminating any unknown pressure torques.The link between SO winds and global buoyancy forcing is explored qualitatively, using salinity and temperature mixed dynamical-box models and a temperature slab model, and semiquantitatively, employing a reduced gravity model which includes parametrized thermodynamics. Our main finding is that, in all of these cases the island geometry implies that the stratification (and, hence, the air–sea heat flux) can always adjust itself to allow the overturning forced by the wind. We find that, in the mixed dynamical-box models, the salinity and temperature differences between the boxes are inversely proportional to the MOC. In spite of the resulting smaller north–south temperature difference, the meridional heat transport is enhanced.