  We consider a system of particles with arms that are activated randomly to
grab other particles as a toy model for polymerization. We assume that the
following two rules are fulfilled: Once a particle has been grabbed then it
cannot be grabbed again, and an arm cannot grab a particle that belongs to its
own cluster. We are interested in the shape of a typical polymer in the
situation when the initial number of monomers is large and the numbers of arms
of monomers are given by i.i.d. random variables. Our main result is a limit
theorem for the empirical distribution of polymers, where limit is expressed in
terms of a Galton-Watson tree.
