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Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel $K_{ij}\\sim ij$, where $ij$ is the product of the sizes of two merging clusters. Here, we study more general cases in which $K_{ij}$ is sub-linear as $K_{ij}\\sim (ij)^{\\omega}$ with $0 \\le \\omega < 1/2$; we find that the percolation transition (PT) is discontinuous. 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