Pendant extensions of sparse clique copies

If $H$ is formed by attaching one pendant edge to a fixed clique, each copy has a unique clique core. Its number of extensions is the number of ambient edges from that core to outside vertices. At a scale where the core count is tight and its expected extension count diverges sufficiently rapidly, a Chernoff bound uniformly over all possible cores shows that the total count, divided by the extension mean, has the same limiting law as the core count. Non-induced copies are intended; extra ambient edges are not forbidden.