Abstract: Provided is a carrier for an olefin polymerization catalyst which carrier comprises a substance obtained by adding a liquid organic compound not dissolving a magnesium halide into a liquid medium having dissolved therein a substance which contains the magnesium halide as at least one component, the liquid medium further containing an oxide of Group II-IV metal or metals in the Periodic Table, followed by cooling to a temperature not higher than 0.degree. C. and subsequent heat treatment at a temperature in the range of 40.degree. to 200.degree. C.

Abstract: Compositions consisting of the reaction product or complex resulting from the mixing of a transition metal compound such as a tetraalkoxy titanium compound and a boron compound such as a trialkyl boron compound are useful in the preparation of catalysts for polymerizing .alpha.-olefins exhibiting ultra-high efficiencies at high polymerization temperatures.