The first synthesis of well-defined star polymers consisting of eight polyisobutylene (PIE) arms emanating from a calixarene core is described. The synthesis was accomplished with the use of octafunctional calixarene derivative initiators which, in conjunction with BCl3/TiCl4 coinitiators, induce the living polymerization of isobutylene(IB). Specifically, the initiators were tert-hydroxy and tert-methoxy derivatives (5 and 6, respectively) of 5,11,17,23,29,35,41,47-octaacetyl-49,50, octamethoxycalix[8]arene. The tert-methoxy derivative (6) is soluble in polymerization charges (CH3Cl/hexanes) at -80 degrees C and was used preferentially. To gain insight into the mechanism of polymerization, model experiments using a monofunctional analogue, 2-(p-methoxyphenyl)-2-methoxypropane (8), of the octafunctional initiators were also conducted. According to these model studies, 8 is an efficient initiator for the living polymerization of IB, and the initiator residue can be spectroscopically quantitated as the head group of PIB. Well-defined stars with close to theoretical composition and molecular weights were obtained in the presence of BCl3-TiCl4 mixtures; however, polymerizations were unsatisfactory with the use of only BCl3 or only TiCl4. Polymerizations were carried out in two stages in one reactor. In the first stage, the reaction was initiated with the 6/BCl3 combination using similar to 25% of the required amount of IB in CH3Cl at -80 degrees C, followed by the second stage, in which hexanes, TiCl4, and the balance of the monomer were added. Gel permeation chromatography, by the use of on-line RI, UV, and laser light scattering detectors, was used to determine the molecular weight and composition of the linear and octa-arm star polymers. The number-average number of arms, <(N)over bar (n,arm)>, and the weight-average number of arms, <(N)over bar (w,arm)>, were determined directly by core destruction of the calixarene moiety, followed by molecular weight determination of the surviving arms; according to these studies, <(N)over bar (n,arm)> and <(N)over bar (w,arm)> were 7.6 and 7.7, respectively.