  We consider the Lifshitz-Slyozov model with inflow boundary conditions of
nucleation type. We show that for a collection of representative rate functions
the size distributions approach degenerate states concentrated at zero size for
sufficiently large times. The proof relies on monotonicity properties of some
quantities associated to an entropy functional. Moreover, we give numerical
evidence on the fact that the convergence rate to the goal state is algebraic
in time. Besides their mathematical interest, these results can be relevant for
the interpretation of experimental data.
