Two different situations corresponding to out-of-equilibrium growth of an a
dsorbate and to equilibrium adsorption of a gas are discussed using the vic
inal face of a transition metal as the substrate. Monte-Carlo simulations i
n the kinetic and equilibrium regimes are applied to the ordering of Xe and
Ag atoms close to the monatomic steps of the (997) vicinal face of platinu
m. It is shown that the steps can favor the growth of one or two rows of ad
atoms (row-by-row growth) in the submonolayer domain, depending on the temp
erature and on intrinsic parameters connected to the magnitude of the inter
actions between the adspecies themselves and between these adspecies and th
e substrate. Such a behavior is consistent with very recent helium atom sca
ttering experiments.