A series of multi-layer numerical experiments show that classical finite amplitude instabilities in boundary currents are not sufficient to account for the pinched-off eddies observed in the ocean and in laboratory experiments. These instabilities (barotropic or baroclinic) are shown to lead to an entrainment of offshore fluid into the boundary currents. Eddy separation, on the other hand, requires an additional process, such as a larger scale of motion containing a downstream velocity convergence of finite amplitude; this might be produced by long period fluctuations in the discharge from an upstream source region which controls the boundary current, or by topographic features. In our spatially idealized model, we numerically computed the temporal evolution of an assumed initial state consisting of a fast moving upstream region separated by a potential vorticity front from a slow moving downstream region. We verify long-wave theories which show that this initial state indeed leads to frontal steepening and to a blocking wave. This eventually produces large transverse velocities followed by complete detrainment of eddies without any entrainment into the residual boundary current.