Catalyst components for the polymerization of olefins, obtained by reacting a tetravalent titanium halide or halogen alcoholate and an electron-donor compound with a solid comprising a porous metallic oxide containing hydroxyl groups on the surface, on which is supported a magnesium dihalide or a magnesium compound which does not contain Mg-C bonds and can be transformed into a dihalide, characterized in that the quantity of Mg supported on the oxide prior to the reaction with titanium compound, and present in the catalyst component after the reaction with the Ti compound, is from 5% to 12% weight with respect to the weight of the catalyst component.
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