  In this paper we consider the coalescence dynamics of a tagged particle
moving in a random distribution of particles with volumes independently
distributed according to a probability distribution (CTP model). We provide a
rigorous derivation of a kinetic equation for the probability density for the
size and position of the tagged particle in the kinetic limit where the volume
fraction $\phi$ filled by the background of particles tends to zero. Moreover,
we prove that the particle system, i.e. CTP model, is well posed for a small
but positive volume fraction with probability one as long as the the
distribution of the particle sizes is compactly supported.
