  We consider a natural destruction process of an infinite recursive tree by
removing each edge after an independent exponential time. The destruction up to
time t is encoded by a partition $\Pi$(t) of N into blocks of connected
vertices. Despite the lack of exchangeability, just like for an exchangeable
fragmentation process, the process $\Pi$ is Markovian with transitions
determined by a splitting rates measure r. However, somewhat surprisingly, r
fails to fulfill the usual integrability condition for the dislocation measure
of exchangeable fragmentations. We further observe that a time-dependent
normalization enables us to define the weights of the blocks of $\Pi$(t). We
study the process of these weights and point at connections with
Ornstein-Uhlenbeck type processes.
