To better understand the aggregation of living polymers formed in anionic polymerization, we develop a theoretical model for the aggregation state of living polymers with polar headgroups in hydrocarbon solvents. In particular, we have examined polymers with butadienyllithium headgroups in benzene. The system is modeled as a population of star-like micelles coexisting with a broadly polydisperse population of long cylindrical micelles. We use numerical solutions of the self-consistent mean-field equations to quantitatively calculate the stretching energy of the polymer chains in the micelles, and semiempirical and ab initio quantum chemistry methods to calculate headgroup geometries and binding energies. We find that the general aggregation state of the model consists of nearly Gaussian-distributed spherical micelles for long polymer chain lengths, which cross over to exponentially-distributed cylindrical micelles at short chain lengths, with a region of coexistence of the two types of micelles in a narrow intermediate range of chain length. For physically reasonable values of the model parameters, the predicted aggregation state is consistent with experimental features observed for this system by Stellbrink , and in particular with the formation of star-like micelles with mean aggregation numbers of 10 or larger.