  In the present paper, the connection between surface order-disorder phase
transitions and the percolating properties of the adsorbed phase has been
studied. For this purpose, four lattice-gas models in presence of repulsive
interactions have been considered. Namely, monomers on honeycomb, square and
triangular lattices, and dimers (particles occupying two adjacent adsorption
sites) on square substrates. By using Monte Carlo simulation and finite-size
scaling analysis, we obtain the percolation threshold $\theta_c$ of the
adlayer, which presents an interesting dependence with $w/k_BT$ (being $w$,
$k_B$ and $T$, the lateral interaction energy, the Boltzmann's constant and
temperature, respectively). For each geometry and adsorbate size, a phase
diagram separating a percolating and a non-percolating region is determined.
