Abstract The localized monolayer adsorption of an atomic adsorbate on a triangular lattice was studied with the help of grand ensemble Monte Carlo simulations. The adsorbed atoms were assumed to interact with one another via a Lennard-Jones potential and interactions up to the sixth nearest neighbours were taken into account. The diameters of the adsorbed atoms (relative to the lattice unit cell size) were chosen such that a direct comparison could be made of the simulation results with the renormalization group calculations due to Ostlund and Berker. In particular, it was assumed that mutual occupation of adjacent sites is excluded because of the highly positive energy of interaction between the first nearest neighbours. In spite of the difficulties due to metastability, several phase diagrams for adsorbed films were constructed and compared with the phase diagrams obtained by the renormalization group method. A remarkable agreement between the results obtained by these two methods was found.