the last time, before a dislocation had definitely separated them. With an appropriate coding of the fragments, one guesses that there should be a natural way to define a genealogy tree, rooted at the initial fragment, associated to any such fragmentation. It would be natural to put a metric on this tree, e.g. by letting the distance from a fragment to the root of the tree be the time at which the fragment disappears.

Conversely, it turns out that trees have played a key role in models involving self-similar fragmentations, notably, Aldous and Pitman [@jpda98sac] have introduced a way to log the so-called Brownian *Continuum Random Tree* (CRT) [@aldouscrt93] that is related to the standard additive coalescent. Bertoin [@bertsfrag02] has shown that a fragmentation that is somehow dual to the Aldous-Pitman fragmentation can be obtained as follows. Let $\mathcal{T }_{B}$ be the Brownian CRT, which is considered as an “infinite tree with edge-lengths” (formal definitions are given below). Let $\mathcal{T }_{t}^{1}, \mathcal{T }_{t}^{2},\ldots $ be the distinct tree components of the forest obtained by removing all the vertices of $\mathcal{T }$ that are at distance less than $t$ from the root, and arranged by decreasing order of “size”. Then the 