The dynamics of a cluster-type system formed by constant total number of molecules, M, is studied when clusters change their sizes by nearest-size transitions (the Szilard model) with time-dependent boundary conditions and non-zero initial cluster size distribution. We compare these results to those reported previously [5], when non-stationary cluster size distribution was considered under the condition that only monomers are present in the system at the initial moment t=0, and describe the effect of arbitrary pre-existing clusters on the time evolution of the interacting clusters with different sizes, n. The average group size problem is also solved, and the process of relaxation in the system is studied.