We present numerical self-consistent field calculations in a two-gradient cylindrical coordinate system for a (translationally restricted) quenched polyelectrolyte star which is electrostatically attracted to an oppositely charged surface with homogeneous surface charge density at a given ionic strength of a 1:1 electrolyte. The results prove that without any additional driving force for adsorption, electrostatic attraction alone can give significant overcompensation of the surface charge provided that the ionic strength is below some critical value. This is demonstrated for the case that the charge density on the surface is lower than the (projected) charge density in the star. In the regime of charge overcompensation, the thickness of the adsorbed layer is of the order of the star size in solution. The adsorbed layer is laterally inhomogeneous and the outer part of the adsorption profile is locally neutralized by the small counterions. (C) 2003 American Institute of Physics.