Hyperbranched polyethene was synthesized using a novel TaCl5/alkylaluminum halide catalyst system. The polymers were viscous oils with a ratio of methyl hydrogens/total alkyl hydrogens of 0.25-0.40 and weight-average molecular weights of 600-4000 daltons. Both branching and molecular weight can be varied by changing reaction conditions and catalyst composition. The system can also be modified to synthesize 1-alkenes (principally, 1-hexene). A second system, involving TiCl4/alkylaluminum halide, also gave hyperbranched polyethene, with a ratio of methyl hydrogens/total alkyl hydrogens of 0.10-0.25. Weight-average molecular weights varied from 900 to 1800 daltons. Higher selectivity to liquid product was achieved through the addition of dihydrogen. The mechanism of the formation of branched polyethene appears to involve, for the most part, oligomerization of ethene to 1-alkenes (principally 1-hexene) by a transition metal alkyl species followed by cationic oligomerization of the 1-alkenes by Lewis acidic species. The addition of tetraalkylammonium chloride to the TaCl5/Et3Al system resulted in a change in product selectivity from all polyethene to >65% 1-hexene. The highly selective trimerization of ethene by the tantalum system is unusual.