An important operational range for TEXTOR-DED is the case of a high ergodization at the plasma edge. Under these conditions, the edge magnetic field forms a proper ergodic layer and a laminar zone. The laminar zone is established by magnetic field lines which intersect wall elements after only a few toroidal turns (open ergodic system). For this, both the heat and particle transport in the plasma edge are dominated by the laminar zone which shows a well defined structure compared with that of the ergodic layer. For the present analysis the regions containing field lines with connection lengths corresponding to one or to two poloidal turns are of particular interest; the radial width of these regions is of the same order as the width of the unperturbed SOL of a `classical' limiter or divertor configuration. Field lines running poloidally twice around the torus introduce a particular new feature, they impose a connection between radially separated areas and thus enhance the radial temperature and particle transport. A new 2-D modelling approach code for the laminar zone of an ergodic divertor has been developed which is strongly oriented on the topology of the magnetic field lines in the plasma edge. A 2-D finite element method is used in order to model the perpendicular transport of particles and energy. For obtaining a solution of the parallel transport, an analytical model is discussed providing expressions for averaged particle and energy sources. By considering the topological properties of the magnetic field and corresponding assumptions in the code, the transport calculation in the perturbed plasma edge gives a first insight into the generic transport properties of the TEXTOR-DED laminar zone. As an important application for later experiments the power fluxes to the wall elements are estimated. They show a strong variation perpendicular to the perturbation coils and a medium variation over the helical divertor footprints.