Most polymers are polydisperse. We extend the self-consistent field polymer adsorption theory due to Scheutjens and Fleer to account for an arbitrary polymer molecular weight distribution with a cutoff chain length N(max). In this paper, the treatment is restricted to homopolymers. For this case a very efficient scheme is proposed for which the enumerations to compute adsorption characteristics for a complete set of molecules {n(i)} is only a factor of 2 larger than for monodisperse polymers with a chain length N(max). For polydisperse polymer, adsorption fractionation takes place, with the long chains preferentially adsorbing from dilute solutions. This fractionation depends on the volume/surface ratio and the polymer concentration; it leads to rounded adsorption isotherms when N(w)/N(n) > 1. It is shown that the hystereses between the adsorption and desorption isotherms, which is often observed, can be explained from an equilibrium point of view. The full calculations corroborate the trends predicted by a simple model proposed by Cohen Stuart et al. In addition, in the numerical method many more details are retained.