A process for production of polyisobutylene includes subjecting a reaction admixture comprising isobutylene, a diluent for the isobutylene, which may be isobutane, and a catalyst composition, that may include a BF3/methanol catalyst complex, to reaction conditions suitable for causing at least a portion of the isobutylene to undergo polymerization to form a polyisobutylene product including polyisobutylene molecules. At least a fraction of the polyisobutylene molecules thus produced have alpha position double bonds and the polyisobutylene product has a number average molecular weight (MN) and a polydispersity index (PDI). The concentration of the diluent in the reaction admixture may be manipulated to control or change any one or more of (a) the relative size of the fraction, (b) the number average molecular weight of the product, (c) the polydispersity index of the product and (d) the relative size of the portion. The diluent concentration may be held constant to maintain any one or more of such characteristics constant.