  The kinetic equations describing irreversible aggregation and the scaling
approach developed to describe them in the limit of large times and large sizes
are tersely reviewed. Next, a system is considered in which aggregates can only
react with aggregates of their own size. The existence of a scaling solution of
the kinetic equations can then be shown rigorously in the case in which the
total mass of the system is conserved. A large number of detailed properties of
the solution, previously predicted by qualitative arguments, can be shown
rigorously as well in this system. In the case in which gelation occurs, some
sketchy rigorous results are shown, and numerical evidence for the existence of
a scaling solution is presented. These are the first explicit examples of
typical scaling behaviour for systems exhibiting gelation.
