The present invention relates to pulverulent solids obtainable by reaction of a metal alkyl compound of a divalent or higher-valent metal and a finely divided support which on its surface bears functional groups which can form a chemical bond between the metal atom of the metal alkyl compound and the surface of the support, wherein the particles of the finely divided support have particle diameters of less than 1000 nm and less than 5% by weight of the metal alkyl compound is extractable in a single extraction of the pulverulent solid with 20 ml of heptane per gram of solid at 50.degree. C. In addition, the invention relates to a process for preparing the pulverulent solids, a catalyst composition for the polymerization of olefins which comprises the pulverulent solids and polymerization processes using the catalyst composition.