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We determine in high anisotropy Pt/Co- and Ni/Co-based multilayer materials, which are candidates for high density storage applications, the contributions to the extraordinary Hall effect. In order to gain more insight into the physics underlying these processes, the dependence of the extraordinary Hall resistivity on the longitudinal resistivity is used to identify the skew scattering and the combined intrinsic and side jump effects when analyzing their variation with temperature. Furthermore, the influence of an additional amorphous CoFeB layer is shown, revealing a possibility to enhance the extraordinary Hall effect using this material.