The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N = 10 to N = 80 and grafting densities σ from 0.025 to 0.20 are considered, both for the "quenched" case, where the anchor points are kept fixed at randomly chosen surface sites, and the "annealed" case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and end monomers are studied and discussed in the light of current theoretical predictions, and it is shown that most of these properties can be understood in terms of appropriate scaling concepts. Both the relaxation of the total chain configurations and the time dependence of monomer mean square displacements are studied. In the annealed case the lateral diffusion constant D is found to behave as D∼σ-qN -p, where q = 2/3 and p crosses over from p≈1 at small σ to p≈2 at large σ. The results for the relaxation time τ are consistent with the recent scaling prediction τ∼σ bNa with a = 3 and b = 2/3.