Irreversible anionic polymerization is revisited with an emphasis on determining the dependence of the MW distribution on initial conditions. It is shown that only two parameters govern the distribution: the ratio of initiation to propagation rate constants and the ratio of initial monomer to initiator concentrations. New and simple criteria are developed that predict the breadth of the MW distribution based on these parameters. Even when initiation is slower than propagation, it is still possible under certain conditions to obtain a narrow, Poisson-like MW distribution. Since it impacts self-assembly of block copolymers into microphases, the compositional variation of block copolymers produced by living polymerization techniques is also analyzed. A somewhat unexpected result is the composition variability in block copolymers can be significant (10-15%) even when the blocks have dispersity indices less than 1.01.