The effects of Coulomb collisions in the transition region between the collision-dominated regime at low altitudes and the collisionless regime at high altitudes have been taken into account to study the escape of H+ ions in the polar wind. A specialized spectral method is used to solve the steady state Fokker-Planck equation describing the diffusion and upward bulk motion of H+ ions through a background of O+ ions. The H+ ion velocity distribution function is determined as a function of altitude for realistic initial conditions in the whole velocity space. We emphasize the importance for a correct choice of the boundary conditions at v = 0 to obtain regular mathematical solutions. The results of this kinetic model are compared with results of earlier polar wind models based on different approximations of the plasma transport equations.