Trialkyl and aryl organoboranes catalyze the polymerization of dimethylsulfoxonium methylide (1). The product of the polymerization is a tris-polymethylene organoborane. Oxidation affords linear telechelic a-hydroxy polymethylene. The polymer molecular weight was found to be directly proportional to the stoichiometric ratio of ylicle/borane, and polydispersities as low as 1.01 - 1.03 have been realized. Although oligomeric polymethylene has been the most frequent synthetic target of this method, polymeric star organoboranes with molecular weights of 1.5 million have been produced. The average turnover frequency at 120 degreesC in 1,2,4,5-tetrachlorobenzene/toluene is estimated at >6 x 106 g of polymethylene (mol boron)(-1) h(-1). The mechanism of the polyhomologation reaction involves initial formation of a zwitterionic organoborane(.)ylide complex which breaks down in a rate-limiting 1,2-alkyl group migration with concomitant expulsion of a molecule of DMSO. The reaction was found to be first order in the borane catalyst and zero order in ylide. DMSO does not interfere with the reaction. The temperature dependence of the reaction rate yielded the following activation energy parameters (toluene, DeltaH(double dagger) = 23.2 kcal/mol, DeltaS(double dagger) = 12.6 cal deg/mol, DeltaG(double dagger) = 19.5 kcal/mol; THF, DeltaH(double dagger) = 26.5 kcal/mol, DeltaS(double dagger) = 21.5 cal deg/mol, DeltaG(double dagger) = 20.1 kcal/mol).