Abstract New multi-arm star block copolymers comprising of rubbery polyisobutylene (PIB) midsegment and glassy polystyrene (PS) end blocks have been synthesized by carbocationic polymerization using a new multifunctional initiator, hexaepoxy squalene (HES), with TiCl 4 coinitiator, di- t-butylpyridine (D tBP) as a proton trap and N, N-dimethylacetamide (DMA) as an electron pair donor in methylcyclohexane (MeCHx)/methyl chloride (MeCl) solvent mixtures at −80 °C. It was found that reaction conditions, such as solvent composition, HES/isobutylene (IB) ratio and TiCl 4 concentration, have profound influence on initiator efficiency and functionality. Living conditions were achieved in the presence of DMA in MeCHx/MeCl 60/40 v/v, while in the absence of DMA, the M n–conversion plot showed a considerable intercept. Depending on the reaction conditions, the PIB midblocks had 3–10 arms. Reaction rates increased with increasing solvent polarity and TiCl 4 concentration. Living narrow molecular weight distribution PIBs ( M w/ M n=1.1–1.2) were reacted with styrene (St) solution containing D tBP and DMA to yield multiarm-star PIB–PS block copolymers. Blocking was evidenced by SEC analysis and copolymers with 8.9–28.6 wt.% PS, M n∼164,000–609,000 g/mol and M w/ M n=1.32–1.88 were successfully synthesized.