sequence $F_{B}(t)$ of these sizes defines as $t$ varies a self-similar fragmentation. A moment of thought points out that the notion of genealogy defined above precisely coincides with the tree we have fragmented in this way, since a split occurs precisely at branchpoints of the tree. Fragmentations of CRT’s that are different from the Brownian one and that follow the same kind of construction have been studied in [@mierfmoins].

The goal of this paper is to show that any self-similar fragmentation process with negative index can be obtained by a similar construction as above, for a certain instance of CRT. We are interested in negative indices, because in most interesting cases when the self-similarity index is non-negative, all fragments have an “infinite lifetime”, meaning that the pieces of the fragmentation remain macroscopic at all times. In this case, the family tree defined above will be unbounded and without endpoints, hence looking completely different from the Brownian CRT. By contrast, as soon as the self-similarity index is negative, a loss of mass occurs, that makes the fragments disappear in finite time (see [@bertafrag02]). In this case, the metric family tree will be a bounded object, and in fact, a CRT. To 