关键词: Uniform recursive tree, branch, limiting behavior

Abstract: The authors consider the limiting behavior of various branches in a uniform
recursive tree with size growing to infinity. The limiting distribution of $\zeta_{n,m}$, the number of branches with size $m$ in a uniform recursive tree of order $n$, converges weakly to a Poisson distribution with parameter $\frac1m$ with convergence of all moments. The size of any large branch tends to infinity almost surely.

Key words: Uniform recursive tree, branch, limiting behavior