  In this work, we introduce the notion of random zooming systems and prove the
existence of equilibrium states for which we call random zooming potentials,
that include the hyperbolic ones, possibly with the presence of a critical set.
The proof follows ideas of the work [4]. With a mild condition, we obtain
uniqueness. We also prove that the classes of random zooming potentials and
random hyperbolic potentials are equivalent and also contain the null
potential, giving measures of maximal entropy.
