  We prove a fluid limit for the coarsening phase of the condensing zero-range
process on a finite number of sites. When time and occupation per site are
linearly rescaled by the total number of particles, the evolution of the
process is described by a piecewise linear trajectory in the simplex indexed by
the sites. The linear coefficients are determined by the trace process of the
underlying random walk on the subset of non-empty sites, and the trajectory
reaches an absorbing configuration in finite time. A boundary of the simplex is
called absorbing for the fluid limit if a trajectory started at a configuration
in the boundary remains in it for all times. We identify the set of absorbing
configurations and characterize the absorbing boundaries.
