The properties of water mass transformation and the thermohaline circulation in shallow marginal seas with topography and subject to surface cooling are discussed in the context of an eddy-resolving primitive equation model and an analytic planetary geostrophic model. A unique and important aspect of the model configuration is that the geostrophic contours, or characteristics of the system, extend from a region where temperature is restored toward a uniform value, providing a source of heat, through the cooling region. This removes a degree of symmetry that has often been imposed in previous studies of deep convection. The heat loss within the marginal sea is balanced by lateral advection from the restoring region. The planetary geostrophic model shows that the basic temperature distribution can be well predicted by integrating along geostrophic contours from their entry into the marginal sea to their exit. Scaling estimates for the exchange rate and density of the waters formed within the marginal sea are derived and compare well with a series of numerical model calculations. In contrast to many previous buoyancy-forced deep convection problems, basin-scale cooling is balanced mainly by the mean flow, with mesoscale eddies serving primarily to restratify locally but not to provide a net heat flux to balance cooling. However, eddy fluxes and the mean flow are locally of comparable importance for cases with a localized patch of surface cooling.