  We consider Smoluchowski's coagulation equation in the case of the diagonal
kernel with homogeneity $\gamma>1$. In this case the phenomenon of gelation
occurs and solutions lose mass at some finite time. The problem of the
existence of self-similar solutions involves a free parameter $b$, and one
expects that a physically relevant solution (i.e. nonnegative and with
sufficiently fast decay at infinity) exists for a single value of $b$,
depending on the homogeneity $\gamma$. We prove this picture rigorously for
large values of $\gamma$. In the general case, we discuss in detail the
behaviour of solutions to the self-similar equation as the parameter $b$
changes.
