Smoluchowki’s coagulation equations describe a wide variety of mass agggregation processes in physical chemistry and physics (polymerization, colloidal separation, aerosol physics, gravitational clustering...). They also arise in population genetics and combinatorics. I will describe simple proofs of optimal results on dynamic scaling in these equations. These involve one-parameter families of self-similar solutions with fat tails, and the characterization of their domains of attraction. This is work with Bob Pego (Maryland).