  The aim of this two-part paper is to investigate the stability properties of
a special class of solutions to a coagulation-fragmentation equation. We assume
that the coagulation kernel is close to the diagonal kernel, and that the
fragmentation kernel is diagonal. In a companion paper we constructed a
two-parameter family of stationary solutions concentrated in Dirac masses, and
we carefully studied the asymptotic decay of the tails of these solutions,
showing that this behaviour is stable. In this paper we prove that for initial
data which are sufficiently concentrated, the corresponding solutions approach
one of these stationary solutions for large times.
