  We consider an extrinsic contribution to the anomalous and spin Hall effect
in dilute alloys based on Fe, Co, Ni, and Pt hosts with different
substitutional impurities. It is shown that a strong skew-scattering mechanism
is absent in such crystals with multi-sheeted Fermi surfaces. Based on this
finding, we conclude on the mutual exclusion of strong intrinsic and
skew-scattering contributions to the considered transport phenomena. It also
allows us to draw general conditions for materials where the anomalous Hall
effect caused by the skew scattering can be achieved giant.
