[en] A 2-D calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses anomalous radial diffusion, including perpendicular ion momentum, and classical cross-field drifts transport. Parallel and perpendicular currents yield a self-consistent electrostatic potential on both sides of the magnetic separatrix. Outside the separatrix, the simulation extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms - from viscosity, charge-exchange and poloidal damping, inertia, and triangledownB - contribute to the determining the potential. The model rigorously enforces cancellation of gyro-viscous and magnetization terms from the transport equations. The results emphasize the importance of E x B particle flow under the X-point which depends on the sign of the toroidal magnetic field. Radial electric field (E_y) profiles at the outer midplane are small with weak shear when high L-mode diffusion coefficients are used and are large with strong shear when smaller H-mode diffusion coefficients are used. The magnitude and shear of the electric field (E_y) is larger both when the core toroidal rotation is co-moving with the inductive plasma current and when the ion triangledownB-drift is towards the single-null X-point