An analytical description of the final stage of diffusive decomposition leaning upon the Slezov theory is developed for several mass transfer mechanisms. The process of formation and relaxation of the crystal size distribution function from the initial ripening stage to its final state corresponding to the universal distribution is studied. The boundary points of a transition region responsible for the tails of the distribution functions on the right of the relevant stopping points are found analytically. The explicit time dependent analytical expressions for the distribution function and particle growth rates are derived with allowance for the plausible mechanisms of mass transfer. (C) 2016 Elsevier B.V. All rights reserved.