The adsorption of long flexible chains from dilute solution is studied by Monte Carlo simulation of a coarse-grained bead-spring model, and the results are interpreted in terms of phenomenological theories, using both mean field approaches and scaling concepts. It is shown that the surface excess, i.e., the integral of the local density difference of the monomers close to the surface relative to the bulk changes its sign very close to the adsorption transition (that is a sharp transition in the limit where the chain length diverges to infinity) for long chains, and it can be described in terms of the standard scaling description that has previously been tested for polymers with one end anchored on the surface ("polymer mushrooms"). Attention is also paid to the question on how this description changes when the temperature T of the polymer solution approaches the theta temperature Theta. Since the theta point can also be considered as an end point of a line of critical points, where the polymer solution phase separates into a dilute solution of collapsed chains and a more concentrated solution in the bulk, the adsorbing wall for T