  We revisit the scaling theory of the Smoluchowski equation with special
emphasis on the dimensional analysis to derive the scaling ansatz and to give
an insightful foundation to it. It has long been argued that the homogeneity
exponent $\lambda$ of the aggregation kernel divides the aggregation process
into two regimes (i) $\lambda\leq 1$ nongelling and (ii) $\lambda>1$ gelling.
However, our findings contradict with this result. In particular, we find that
the Smoluchowski equation is valid if and only if $\lambda<1$. We show that
beyond this limit i.e. at $\lambda\geq 1$, it breaks down and hence it fails to
describe a gelation transition. This also happens to be accompanied by
violation of scaling.
