We study in this work a competitive reaction model between monomers on a catalytic surface. The surface is represented by a square lattice and we consider the following reactions: A+A(B)-->A(2)(AB), where A and B are two monomers that arrive at the surface with probabilities y(A) and y(B), respectively. The model is studied in the adsorption controlled limit, and every time a monomer A or B lands on the surface it occupies a single empty site of the lattice. When a A monomer sits on the surface, it stays there unless it finds another A or B monomer. In this case the reaction occurs instantaneously leaving two new vacant sites on the lattice. The reactions between two A monomers and between A and B monomers are assumed to happen with the same probability. The model is studied in the site and pair mean-field approximations as well as through Monte Carlo simulations. We show that the model exhibits a continuous phase transition between an active and a B-absorbing state, when the parameter y(A) is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis at the critical point are used to determine the critical exponents beta, nu(perpendicular to), and nu(parallel to). Our results seem to confirm that this reaction model is in the same universality class of the directed percolation in (2+1) dimensions.