A simple one-dimensional model for plasma deposition in a rectangular showerhead reactor with single side pumping has been developed in order to explain the mechanisms which yield uniform deposition using this gas flow configuration. Although the flow velocity increases linearly with distance towards the pumping side, the solution of the transport equations for the neutral species shows that their number densities are constant throughout the reactor. Consequently, the plasma and surface deposition reactions are independent of position in any arbitrarily-large-area showerhead reactor.