We consider a discrete model of coagulation, where links between particles are created independently at some fixed rate, except that links with "large" clusters are forbidden. It is known that the concentrations in this model converge to the solution of Smoluchowski's equation with a multiplicative kernel. The discrete model contains much more information than the continuous equation, and therefore allows to observe finer features, such as the shape of the clusters. In particular, this model exhibits self-organized criticality, in that, after time 1, a typical cluster in solution is a critical Galton-Watson tree.