This invention is intended to synthesize a multi-branched polymer, which has an uniform molecular chain lengths and is free from branch defects, without the need for purification. This invention is also intended to synthesize a polyfunctional radical polymerization initiator represented by Formula 1: wherein n is an integer of 1 or larger; Y is a polyfunctional unsaturated compound; R1 is a hydrocarbon group; R2 is a structure in which one molecule of a radically polymerizable unsaturated hydrocarbon compound is bound to R1 and the oxygen atom; X1 of B—X1 (boron-X1) bond is an alkoxy or phenyl group; and X2 of B—X2 (boron-X2) bond is an alkoxy or phenyl group.