  We present a stochastic evolutionary model obtained through a perturbation of
Kauffman's maximally rugged model, which is recovered as a special case. Our
main results are: (i) existence of a percolation-like phase transition in the
finite phase space case; (ii) existence of non self-averaging effects in the
thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the
space of all possible evolutions, analogous to that of a geometrically broken
object. Thus the model turns out to be exactly solvable in the thermodynamic
limit.
