  It is known in thin-film deposition that the density of nucleated clusters
$N$ varies with the deposition rate $R$ as a power law, $N \sim R^\alpha$. The
exponent $\alpha$ is a function of the critical nucleus size $i$ in a way that
changes with the aggregation-limiting process active in a given system. We
extend here to generic aggregation-limiting processes the derivation of the
analytical capture-zone distribution function $P_\beta(s) = a_\beta s^\beta
\exp(-b_\beta s^2)$ of Pimpinelli and Einstein [Phys. Rev. Lett. 99, 226102
(2007)]. We show that the exponent $\beta$ is generally related to the critical
nucleus size $i$ and to the exponent $\alpha$ by the equality $\alpha (2\beta +
d_f - 2) = 2i$ where $d_f$ is the fractal dimensionality of the clusters. This
remarkable results allows one to measure $i$ with no a priori knowledge of the
actual aggregation mechanism. We apply this equality to measuring the critical
nucleus size in pentacene deposition on mica.
