This paper makes a detailed reappraisal of earlier publications and much unpublished data on the polymerization by HClO4 over the temperature range 25 degrees C to - 97 degrees C. The chief conclusions are: (i) The characteristic bimodal molar-mass distributions found in polymers at temperatures down to about - 30 degrees C are not the result of intrinsic independence between propagating species, but of the intervention of irreversible transfer processes. (ii) The 'common-anion' effect of added Bu(4)NClO(4), on both the transient ionic concentration detectable at low temperatures, and on the yields and rates of polymerization, can be analysed to show the links between the rapid non-equilibrium precursor phase and the subsequent steady phase. In that phase, the reactions are shown, by the number-average molar mass (($) over bar M(n)) the polymer, to have the kinetic character of a 'dormant-living' polymerization, near-ideal at ca. -70 degrees C, but deviating increasingly as transfer increases and finally dominates over the reversible termination process. (iii) That termination process is envisaged as 'ion-pair collapse', the anion of the pair being 'homoconjugated' with a molecule of the acid, which is released on collapse. This mechanism, proposed by Szwarc, offers a satisfactory resolution of the 'pseudo' cationic controversy, interpreting the polymer ester molecules, not as propagating species, but as the reservoir from which propagating ion-pairs are generated by acid-activation.