The authors examine theoretically the effect of electrostatics on the self-assembly of charged cylindrical micelles which behave as living polymers. The growth of micelles as a function of increasing surfactant and/or electrolyte concentration exhibits three distinct regimes. The most striking feature of the growth law is the existence of a dilute regime, (i), in which the average micelle size varies slowly with concentration. At high concentrations, regimes (ii) and (iii) are characterized by more rapid growth than for neutral micelles. This may be responsible, in part, for the anomalous scaling of rheological properties, as observed in recent experiments.