Conformations and structural transitions of polyelectrolytes strictly confined onto a spherical 2D surface have been investigated by scaling descriptions based on physical arguments concerning polyelectrolyte adsorption onto planar surface and liquid crystals as well as by Monte Carlo simulations using a bead-spring model with short-range and electrostatic repulsions. In case of the electrostatic screened regime, a disordered-ordered (spiral) transition at increasing persistence length of the chain was found. It was predicted that the transition occurred when the persistence length is comparable with the mean spacing between adjacent strands of the ordered chain. The presence of a non-screened electrostatic repulsion led to a more complex behavior with i) a re-entrant order-disorder transition and ii) a tennis ball texture as an additional smectic/nematic structure. The various competing structures given by the theory were recovered by the Monte Carlo simulations, which also indicated that the tennis ball texture was favored over the spiral structure by the long-range interactions for semi-flexible chains.