In this work, a model for the RAFT polymerization following the slow fragmentation approach was developed in order to obtain the full molecular weight distribution (MWD) using probability generating functions (pgf). A combination of univariate and bivariate pgf is applied to deal with the univariate chain length distributions of macroradical, dormant and dead polymer chains, and the bivariate distribution of the two arms intermediate adduct. This allows rigorous modeling of the polymerization system without simplifying assumptions. For comparison purposes, the population balances were solved by direct integration of the resulting equations. Our results show that the pgf technique allows obtaining an accurate solution efficiently in terms of computational time. What is more, the model provides a detailed characterization of the polymer that could be of great help for grasp the process fundamentals. (C) 2014 Elsevier Ltd. All rights reserved.