An isopycnal, two-layer, idealized model for a convective basin is proposed, consisting of a convecting, interior region and a surrounding boundary current (buoyancy and wind-driven). Parameterized eddy fluxes govern the exchange between the two. To balance the interior buoyancy loss, the boundary current becomes denser as it flows around the basin. Geostrophy imposes that this densification be accompanied by sinking in the boundary current and hence by an overturning circulation. The poleward heat transport, associated with convection in the basin, can thus be viewed as a result of both an overturning and a horizontal circulation. When adapted to the Labrador Sea, the model is able to reproduce the bulk features of the mean state, the seasonal cycle, and even the shutdown of convection from 1969 to 1972. According to the model, only 40% of the poleward heat (buoyancy) transport of the Labrador Sea is associated with the overturning circulation. An exact solution is presented for the linearized equations when changes in the boundary current are small. Numerical solutions are calculated for variations in the amount of convection and for changes in the remotely forced circulation around the basin. These results highlight how the overturning circulation is not simply related to the amount of dense water formed. A speeding up of the circulation around the basin due to wind forcing, for example, will decrease the intensity of the overturning circulation while the dense water formation remains unvaried. In general, it is shown that the fraction of poleward buoyancy (or heat) transport carried by the overturning circulation is not an intrinsic property of the basin but can vary as a result of a number of factors.