  We consider a Bernoulli bond percolation on a random recursive tree of size
$n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It
is known that with high probability, there exists then a unique giant cluster
of size $G_n\sim \e^{-c}$, and it follows from a recent result of Schweinsberg
\cite{Sch} that $G_n$ has non-gaussian fluctuations. We provide an explanation
of this by analyzing the effect of percolation on different phases of the
growth of recursive trees. This alternative approach may be useful for studying
percolation on other classes of trees, such as for instance regular trees.
