Abstract: The present invention relates to catalyst supports for the polymerization and co-polymerization of alpha-olefins, especially ethylene and propylene, consisting essentially of magnesium chloride, characterized in that these supports contain a chlorinated compound of aluminium in a quantity such that the atomic ratio of Al/Mg is comprised between 0.001 and 0.1 and that they occur in the form of spheroidal particles having a mean diameter by mass comprised between 10 and 100 microns and a narrow and controllable particle size distribution such that the ratio of the mean diameter by mass to the mean diameter by number of particles is less than or equal to 3, and also a process for the preparation of these supports.