In this work, the weak polyelectrolyte (PE) adsorption on a strong cationic surface is studied with constant pH Monte Carlo simulations using a coarse-grained model. When a large number of PE chains is added to the system, the PE adsorbed amount vs pH curve exhibits a nonmonotonic behavior, with the appearance of a maximum close to the intrinsic p -value of the PE titratable groups. The apparent p -value of the PE chains shows a non-trivial tendency depending on the pH-value and the surface coverage degree. In increasing the pH-value, the small anions that accompany the cationic surface are replaced by PE chains and small cations. For pH > ~ p + 1, an evident charge reversion of surface is observed. These results are explained analyzing the interplay between the attractive and repulsion electrostatic interactions between the different components of the system (inter- and intra-charged monomers of PE chains, the strong cationic surface and small ions) and their effects on the PE chain ionization.