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We consider inhomogeneous percolation on a hierarchical configuration modelwith a heavy-tailed degree distribution. This graph is the configuration modelwhere all the half-edges are colored either black or white, and edges areformed by uniformly matching edges of the same color. When only the whitehalf-edges are paired, we provide sufficient conditions for the size and totalnumber of incident black half-edges of the connected components to converge inan $\ell^2$-sense. The limiting vector is described by an $\mathbb{R}^2$-valuedthinned L\'{e}vy process. We also establish an $\ell^2$-limit for the number ofvertices in connected components when a critical proportion of the black edgesare included. A key part of our analysis is establishing a Feller-type propertyfor the multiplicative coalescent with mass and weight recently studied in(Dhara et. al 2017, Dhara et. al 2020).

Inhomogeneous percolation on the hierarchical configuration model with a heavy-tailed degree distribution