The Ziegler-Natta system Cp*TiMe3/B(C6F5)(3) catalyzed the copolymerization of ethylene and 1-hexene in toluene into materials that were characterized by H-1 and C-13{H-1} NMR spectroscopy, differential scanning calorimetry, and gel permeation chromatography. The effects of temperature and ethylene/1-hexene and olefin/catalyst ratios on catalyst activities and copolymer molecular weights and molecular weight distributions were studied; the ethylene proportions varied from less than 5% to 85% or more. In addition, significant amounts of 1-hexene were incorporated into the growing polymer chain in a 2,1-fashion; consequently, conventional C-13 NMR analytical methodologies for deducing monomer proportions and dispersions and polymer microstructures, based on a low 1,2-incorporation of ol-olefin, did not work very well. A soluble (in toluene at ambient temperature) but very high molecular weight (weight-average molecular weight similar to 8 x 10(5), weight-average molecular weight/number-average molecular weight = 1.8) rubbery copolymer that formed at -78 degrees C exhibited a predominantly alternating microstructure.