We investigate the complexation of a highly charged sphere with a long flexible polyelectrolyte, both negatively charged in a salt-free environment. Electroneutrality is insured by the presence of divalent counterions. Using molecular dynamics within the framework of the primitive model, we consider different Coulomb coupling regimes. At strong Coulomb coupling we find that the adsorbed chain is always confined to the colloidal surface but forms different conformations that depend on the linear charge density of the chain. A mechanism involving the polyelectrolyte overcharging is proposed to explain these structures. At intermediate Coulomb coupling, the chain conformation starts to become three-dimensional, and we observe multilayering of the highly charged chain while for lower charge density the chain wraps around the colloid. At weak Coulomb coupling, corresponding to an aqueous solvent, we still find like-charge complexation. In this latter case the chain conformation exhibits loops.