Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent, conditions The simulations spanned a wide range of chain lengths, N (100-1000 i.e, up to molecular weights of a few hundred thousands), and anchoring densities, sigma (2 x 10(-4) to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage sigma* = sigma pi R-g(2) is the most appropriate variable that, quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R-g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for sigma* > 8. (C) 2009 Wiley Periodicals, Inc J Polym Sci Part B Polym Phys 47 2449-2461, 2009