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For a random recursive tree of size $n$, let every site have probability ${p \\in (0,1)}$ to remain and with probability $(1-p)$ to be removed. As $n\\to\\infty,$ we show that the proportion of the remaining clusters of size $k$ is of order $k^{-1-\\frac{1}{p}}$, resulting in a Yule-Simon distribution; the largest cluster size is of order $n^{p}$, and admits a non-trivial scaling limit. 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