Star-shaped polymers (4) of alkyl vinyl ethers [CH2=CHOR; R = C2H5, CH2CH(CH3)2] were prepared in high yield on the basis of the living cationic polymerization by the HI/ZnI2 initiating system. For example, isobutyl vinyl ether (IBVE) was polymerized by HI/ZnI2 at -40-degrees-C in toluene into a living polymer, which was subsequently allowed to react with a small amount of a divinyl ether [1a; CH2=CHOCH2CH2OC6H4C(CH3)2C6H4OCH2CH2OCH=CH2]. The resulting star-shaped polymers were completely soluble and consisted of a cross-linked core of poly(1a) to which nearly monodisperse poly(IBVE) chains were radially attached. The number of arms ranged from 3 to 60 per molecule and could be controlled by the arm's chain length, the mole ratio of the divinyl ether to the living end, and the overall concentration of the living end. When a divinyl ether with a flexible spacer (CH2=CHOCH2CH2OCH=CH2, etc.) was employed, however, the yield of star polymers sharply decreased. A similar phenomenon was observed when a living polymer of a bulky vinyl ether (CH2=CHO-n-C16H33) was employed. These effects of reaction conditions were discussed relative to the mechanism of the star polymer formation.