  In this paper we study the existence phase transition of scale invariant
random fractal models. We determine the exact value of the critical point of
this phase transition for all models satisfying some weak assumptions. In
addition, we show that for a large subclass, the fractal model is in the empty
phase at the critical point. This subclass of models includes the scale
invariant Poisson Boolean model and the Brownian loop soup. In contrast to
earlier results in the literature, we do not need to restrict our attention to
random fractal models generated by open sets.
