The complexation between a charged polymer and an oppositely charged spherical particle is investigated using Monte Carlo simulations. Electrostatic interactions are described in the Debye-Huckel approximation. The influence of particle size and ionic concentration on the adsorption/desorption limit, interfacial structure of the adsorbed layer, amount of adsorbed polymer, and the overcharging issue is investigated. Attention is focused on polyelectrolyte adsorption on small spherical particles whose surface curvature effects are expected to limit the amount of adsorbed monomers, large particles that allow the polyelectrolyte to spread to the same extent as on a flat surface, and particles whose radius is close to the polyelectrolyte radius of gyration so that the chain can completely wrap around it. The formation of a polyelectrolyte/particle complex and the conformations of the adsorbed polyelectrolyte are found to result from two competing effects: the electrostatic repulsions between the chain monomers which force the polyelectrolyte to adopt extended conformations and limit the number of monomers which may be attached in particular to small particles, and the electrostatic attractive interactions between the particle and the monomers forcing the charged polymer to undergo structural transition and collapse at the particle surface. It is shown that adsorption is favored by increasing particle size and decreasing ionic concentration. Trains are favored at low ionic concentrations while loops (prior desorption) are favored more when increasing the ionic strength. Below a critical particle size, by decreasing the ionic strength, electrostatic repulsions between the adsorbed monomers force the polyelectrolyte to form protuding tails in solution, hence decreasing the amount of polyelectrolyte adsorption. By decreasing the particle size still further, the low ionic concentration regime is dominated by monomer-monomer repulsions; the polymer partially wraps around or becomes tangential to the particle and two tails extend in opposite directions. The complex may or may not exhibit charge inversion depending on the particle size and ionic concentration. We find that charge reversal increases with salt concentration and reaches a maximum when the polyelectrolyte is able to wrap around the particle completely.