The standard model for the two dimensional simulation of the scrape-off layer (SOL) in the divertor is based on the equations for anomalous cross-field particle and energy transport and classical parallel transport. Recently, it has been complemented by the fluid equations of Braginskii to include all classical fluxes in a self-consistent way. The main physical effect of introducing classical fluxes is the appearance of two new terms - an electrical ExB drift and a diamagnetic B¥P drift, as well as B¥T contributions to the energy transport. Although the new models provide an adequate consideration of all the classical fluxes inside the plasma, a mistake has typically been made in the literature in formulating the new boundary conditions. The poloidal component of the B¥Pi drift, existing inside the plasma, was assumed to continue through to the target surface, thus altering the Bohm criterion. Likewise, the poloidal current due to the B¥(Pi+Pe) term was assumed to reach the surface, changing the surface electric potential drop. In this paper we demonstrate, however, that the diamagnetic fluxes in the whole plasma, including the SOL region, in their major part can be represented by the curl of a vector and, therefore, are self-terminating. We have made a detailed analysis of the distribution of plasma pressure and fluxes at the boundary between the plasma and the surface, encompassing the magnetic presheath and Debye sheath layers. After entering the presheath entrance, the poloidal component of the diamagnetic flux is diverted in the direction along the material surface due to the sharp pressure gradient in the presheath region. This creates boundary drift flows along the surface. Because of that conversion of the poloidal diamagnetic fluxes into boundary fluxes they do not deliver particles and current to the surface and therefore must not be included in the modified boundary conditions. Kinetic analysis of the distribution of the fluxes near the target also reveals an additional ExB drift in the radial direction, which mainly affects the ions motion in the magnetic presheath and Debye sheath layers. This drift is expected to shift the density profile of the plasma near the target in the radial direction on a distance of the order of the ion poloidal Larmor radius.