A solution of a mechanistic puzzle is reported: upon initiation with air at 25 degrees C or with di-tert-butyl peroxide at 80 degrees C, isobutylene (TB) polymerizes at 1 atm in weakly coordinating solvents containing 10 wt % LiCB11(CH3)(12) to a mixture of highly branched (b-PIB) and linear (l-PIB) polyisobutylene. The former polymer is separable by solvent extraction and is identical with the b-PIB that is produced from IB as a sole product under similar conditions under nonwadizing radical initiation with azo-tert-butane. The latter polymer differs from standard l-PIB in that it carries a carborane anion attached at the chain end. The molecular weight of b-PIB ranges up to 26000, and that of l-PIB, up to 50000. Evidence is presented that the concurrent polymerization of TB to b-PIB and l-PIB is launched by an initial oxidation of the CB11(CH3)(12)(-) anion to a neutral radical CB11(CH3)(12)(center dot). This radical is proposed to subsequently transfer a methyl radical to IB, thus launching the formation of b-PIB by the radical mechanism while leaving behind the borenium ylide CB11(CH3)(11), which is a strong Lewis acid and induces simultaneously the formation of l-PIB by the cationic mechanism.