  We present a new a-priori estimate for discrete coagulation-fragmentation
systems with size-dependent diffusion within a bounded, regular domain confined
by homogeneous Neumann boundary conditions. Following from a duality argument,
this a-priori estimate provides a global $L^2$ bound on the mass density and
was previously used, for instance, in the context of reaction-diffusion
equations.
  In this paper we demonstrate two lines of applications for such an estimate:
On the one hand, it enables to simplify parts of the known existence theory and
allows to show existence of solutions for generalised models involving
collision-induced, quadratic fragmentation terms for which the previous
existence theory seems difficult to apply. On the other hand and most
prominently, it proves mass conservation (and thus the absence of gelation) for
almost all the coagulation coefficients for which mass conservation is known to
hold true in the space homogeneous case.
