Size of the largest cluster under zero-range invariant measures

We study the finite zero-range process with occupancy-dependent rate function g(.). Under the invariant measure, which can be written explicitly in terms of g, particles are distributed over sites and we regard all particles at a fixed site as a cluster. In the density one case, that; is, equal numbers of particles and sites, we determine asymptotically the size of the largest cluster, as the number of particles tends to infinity, and determine? its dependence on the rate function.