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

A system of grabbing particles related to Galton-Watson trees