We report the dependence of giant magnetoresistance on the number of bilaye
r repeats in a Co/Cu (001) multilayer. Starting from spin-density functiona
l theory, the electronic structure is described by means of a screened Korr
inga-Kohn-Rostoker method for freestanding multilayer slabs. The in-plane t
ransport is calculated solving the linearized Boltzmann equation in relaxat
ion-time approximation. It is shown that the length scale on which giant ma
gnetoresistance rises is not caused by the intrinsic finite-size effects of
the multilayer slab, but by diffusive surface scattering.