Grafted adsorbing polymers are investigated with the Scheutjens-Fleer self-consistent field model. The surface pressure of such systems is calculated numerically and semiquantitative agreement is found with experimental surface pressure isotherms of PS-PEO diblock copolymers at the air/water interface. Scaling relationships of mean-field models predict the surface pressure pi and the height H of neutral brushes to scale as pi similar to sigma(5/3) and H similar to sigma(1/3), respectively, as a function of the grafting density sigma. These scaling relationships for the surface pressure and the thickness are corroborated experimentally for long PEO chains, provided contributions to pi due to adsorption to the air-water interface are taken into account. In the SCF model the pancake-brush transition in a good solvent is found to be continuous for all chain lengths and adsorption energies. At high adsorption energies the transition is abrupt and resembles a continuous phase transition close to a critical point, a so-called lambda-transition.