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A simple point-vortex “heton” model is used to study localized ocean convection. In particular, the statistically steady state that is established when lateral buoyancy transfer, effected by baroclinic instability, offsets the localized surface buoyancy loss is investigated. Properties of the steady state, such as the statistically steady density anomaly of the convection region, are predicted using the hypothesis of a balance between baroclinic eddy transfer and the localized surface buoyancy loss. These predictions compare favorably with the values obtained through numerical integration of the heton model. The steady state of the heron model can be related to that in other convection scenarios considered in several recent studies by means of a generalized description of the localized convection. This leads to predictions of the equilibrium density anomalies in these scenarios, which concur with those obtained by other authors. Advantages of the heton model include its inviscid nature, emphasizing the independence of the fluxes affected by the baroclinic eddies from molecular processes, and its extreme economy, allowing a very large parameter space to be covered. This economy allows us to examine more complicated forcing scenarios: for example, forcing regions of varying shape. By increasing the ellipticity of the forcing region, the instability is modified by the shape and, as a result, no increase in lateral fluxes occurs despite the increased perimeter length. The parameterization of convective mixing by a redistribution of potential vorticity, implicit in the heton model, is corroborated; the heton model equilibrium state has analogous quantitative scaling behavior to that in models or laboratory experiments that resolve the vertical motions. The simplified dynamics of the heton model therefore allows the adiabatic advection resulting from baroclinic instability to be examined in isolation from vertical mixing and diffusive processes. These results demonstrate the importance of baroclinic instability in ...