  We report results from a molecular dynamics (MD) simulation on the
conformations of a long flexible polyelectrolyte complexed to a charged sphere,
\textit{both negatively charged}, in the presence of neutralizing counterions
in the strong Coulomb coupling regime. The structure of this complex is very
sensitive to the charge density of the polyelectrolyte. For a fully charged
polyelectrolyte the polymer forms a dense two-dimensional "disk", whereas for a
partially charged polyelectrolyte the monomers are spread over the colloidal
surface. A mechanism involving the \textit{overcharging} of the polyelectrolyte
by counterions is proposed to explain the observed conformations.
