  We continue the study initiated by Jean Bertoin in 2012 of a random dynamics
on the edges of a uniform Cayley tree with $n$ vertices in which, successively,
each edge is either set on fire with some fixed probability $p_n$ or fireproof
with probability $1-p_n$. An edge which is set on fire burns and sets on fire
its flammable neighbors, the fire then propagates in the tree, only stopped by
fireproof edges. We study the distribution of the proportion of burnt and
fireproof vertices and the sizes of the burnt or fireproof connected components
as $n \to \infty$ regarding the asymptotic behavior of $p_n$.
