The authors investigate the spreading stage of the deep ocean convection for a strip-shaped convective region to study the law of spreading and sensitivity of the eddy exchange efficiency parameter to the shape of the region and the background stratification. To simulate this convection process a two-layer quasigeostrophic model is used and the input of buoyancy due to surface cooling is parameterized through creation of pairs of baroclinic point vortices with opposite signs of potential vorticity (hetons) at a constant rate. It is shown that the eddy exchange efficiency parameter for lateral fluxes of potential density out of the convective region is not universal but essentially depends on the shape of the region and the relative layer thicknesses. The horizontal spreading of the potential density anomaly shows a faster than diffusive, quasi-linear dependence on time at moderate values of the surface buoyancy flux. This behavior is due to the specific dynamics of hetons and heton clusters.