Monte Carlo simulations are used to study in the Debye-Huckel approximation the complexation between a polyelectrolyte and an oppositely charged spherical particle. Attention is focused on the effect of chain length and ionic concentration on (i) the adsorption/desorption limit, (ii) the interfacial structure of the adsorbed layer, and (iii) the overcharging issue. In particular, we are interested in polyelectrolyte adsorption on particles whose surface area is small to allow the polyelectrolyte to spread to the same extent on a flat surface. The extent of polyelectrolyte adsorption is found to be the result of two competing effects: the electrostatic repulsion between the chain monomers which forces the polyelectrolyte to adopt extended conformations in solutions and limits the number of monomers which may be attached to the particle, and the electrostatic attractive interactions between the particle and the monomers forcing the chain to undergo a structural transition and collapse at the particle surface. To overcome the loss of entropy per monomer due to adsorption, it is shown that a stronger electrostatic attraction, with decreasing ionic concentration, is needed for the short chains. Below that critical ionic concentration, it is found that the degree of adsorption increases with the decrease in both the chain length and ionic strength. Trains are favored at low degrees of chain polymerization while loops are favored more when increasing the size of the chain. Above a critical chain length, electrostatic repulsions between the adsorbed monomers force the polyelectrolyte to form a protuding tail in solution. Charge inversion is also observed. Indeed, depending on the polyelectrolyte length, the number of monomers close to the particle surface is higher than it is necessary to neutralize it. Charge inversion is found to increase with the ionic concentration of the solution.