This work presents exact expressions for size distributions ofweak/multilayer connected components in two generalisations of theconfiguration model: networks with directed edges and multiplex networks witharbitrary number of layers. The expressions are computable in a polynomialtime, and, under some restrictions, are tractable from the asymptotic theorypoint of view. If first partial moments of the degree distribution are finite,the size distribution for two-layer connected components in multiplex networksexhibits exponent $-\frac{3}{2}$ in the critical regime, whereas the sizedistribution of weakly connected components in directed networks exhibits twocritical exponents, $-\frac{1}{2}$ and $-\frac{3}{2}$.
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