The overall objective of this research is the creation of novel star polymers consisting of well-defined stable cores out of which radiate multiple poly(isobutylene-co-styrene) [P(IB-co-St)] arms whose glass-transition temperature (T-g) can be controlled over a wide range (-73 to +100 degreesC) and whose arm termini are fitted with multipurpose (e.g., crosslinkable) functionalities. The first article of this series relates the synthesis and characterization of azeotropic IB/St copolymers [P(IB-aze-St)], which are to be subsequently used as end-functional arms of the target stars. The P(IB-aze-St)s are models for statistical IB/St copolymers. The azeotropic composition is 21/79 (mol/mol) IB/St, and NMR, Fourier transform infrared, and gel permeation chromatography techniques demonstrate copolymer compositional homogeneity over the 12-96% conversion range. Conditions were developed for living azeotropic IB/St copolymerization. The livingness of the azeotropic copolymerization was proven by kinetic investigations. P(IB-aze-St)s with number-average molecular weights of up to 24,000 g/mol and polydispersity indices (weight-average molecular weight/number-average molecular weight) less than 1.5 were prepared. The copolymerization reactivity ratios were determined: r(IB) = 3.41 +/- 0.23 and r(St) = 1.40 +/- 0.26. The effect of the P(IB-aze-St) molecular weight on T,was studied by DSC. T,increases linearly with the number-average molecular weight and reaches a plateau at 62 degreesC at 24,000 g/mol. The heat stability of P(IB-aze-St) was investigated by thermogravimetric analysis, and a 5% weight loss was found at 250 degreesC in air.