  We consider Bernoulli bond percolation on a large scale-free tree in the
supercritical regime, meaning informally that there exists a giant cluster with
high probability. We obtain a weak limit theorem for the sizes of the next
largest clusters, extending a recent result for large random recursive trees.
The approach relies on the analysis of the asymptotic behavior of branching
processes subject to rare neutral mutations, which may be of independent
interest.
