  Similar to topological spaces, we introduce the Cantor-Bendixson rank of a
tree $T$ by repeatedly removing the leaves and the isolated vertices of $T$
using transfinite recursion. Then, we give a representation of a tree $T$ as a
leafless tree $T^\infty$ with some leafy trees attached to $T^\infty$. With
this representation at our disposal, we count the siblings of a tree and obtain
partial results towards a conjecture of Bonato and Tardif.
