  Polymer chains undergoing a continuous adsorption-desorption transition are
studied through extensive computer simulations. A three-dimensional
self-avoiding walk lattice model of a polymer chain grafted onto a surface has
been treated for different solvent conditions. We have used an advanced
contact-density chain-growth algorithm, in which the density of contacts can be
directly obtained. From this quantity, the order parameter and its fourth-order
Binder cumulant are computed, as well as the corresponding critical exponents
and the adsorption-desorption transition temperature. As the number of
configurations with a given number of surface contacts and monomer-monomer
contacts is independent of the temperature and solvent conditions, it can be
easily applied to get results for different solvent parameter values without
the need of any extra simulations. In analogy to continuous magnetic phase
transitions, finite-size-scaling methods have been employed. Quite good results
for the critical properties and phase diagram of very long single polymer
chains have been obtained by properly taking into account the effects of
corrections to scaling. The study covers all solvent effects, going from the
limit of {\it super-self-avoiding walks}, characterized by effective
monomer-monomer repulsion, to poor solvent conditions that enable the formation
of compact polymer structures.
