The MWD moments are derived for a "living" polymerization process which proceeds via active and "dormant" species and where addition of a catalyst, C, to a "dormant" species, P’, leads to the formation of an active species, P*, and another product, E. Such a mechanism is applicable to the "dissociative" mechanism of group transfer polymerization (GTP), where the active species is an enolate and E is a silyl ester, to "living" cationic polymerization, where P* is a free cation and E is the counterion, and to atom transfer radical polymerization (ATRP), where P’ and P* are a covalent species and a free radical, respectively, and C and E are transition metal salts of fewer and higher oxidation states, respectively. Both equilibrium and nonequilibrium initial conditions are used for the calculation. The results are very similar to those obtained for the "associative" mechanism of GTP (corresponding to the generation of ion pairs in cationic polymerization) and for degenerative transfer (i.e., direct exchange of activity between active and "dormant" species). In the absence of added E, the dominating parameter, beta, is defined as beta = alpha k(2)/(p) where k(2) and K-p are the rate constants of reversible deactivation and propagation, respectively, and alpha is the fraction of active chain ends. The value of a in turn depends on the equilibrium constant K and the ratio of initial concentrations of catalyst and initiator, C-0/I-0. In contrast, for the "associative" mechanism of GTP (or ion pair generation in cationic polymerization) the parameter was defined as beta = k(2)/(k(p)I(0)), depending on initiator concentration alone, whereas for degenerative transfer it was beta = K-ex/k(p), irrespective of reagent concentrations. Again, for beta > 1 the polydispersity index decreases with monomer conversion (after a marked increase at low conversions), coinciding with a common observation in group transfer and cationic polymerizations. In a limiting case, at full conversion, M(w)/M(n) approximate to 1 + 1/beta. Differences between equilibrium and nonequilibrium initial conditions can only be seen for beta < 1. Added E (e.g., "livingness enhancer" in GTP) always leads to narrower MWD’s. The results are discussed with respect to GTP using nucleophilic catalysts and to the cationic polymerization of various monomers. The accessible results indicate that the predominant mechanism for activity exchange in GTP and perhaps also in cationic polymerization is degenerative transfer whereas the mechanism for generation of active species from inactive ones has to be determined from analysis of the kinetic reaction orders.