  We extend the theory of the surface-induced magnetic anisotropy to mesoscopic
samples with arbitrary geometry. The shape-induced anisotropy of impurity spins
in small brick-shaped grains of dilute magnetic alloys is studied in detail.
The surface-induced blocking of a magnetic-impurity spin is shown to be very
sensitive to geometric parameters of a grain. This implies that the apparent
discrepancy between the experimental data of different groups on the size
dependence of the Kondo resistivity can result from different microstructure of
the used samples. In order to interpret recent experimental data on the
anomalous Hall effect in thin polycrystalline Fe doped Au films, we analyse the
magnetisation of impurity spins as a function of the impurity position and of
the grain shape.

Mesoscale and Nanoscale Physics