  In the context of f(R) generalizations to the Holst action, endowed with a
dynamical Immirzi field, we derive an analytic solution describing
asymptotically anti-de Sitter black holes with hyperbolic horizon. These
exhibit a scalar hair of the second kind which ultimately depends on the
Immirzi field radial behaviour. In particular, we show how the Immirzi field
modifies the usual entropy law associated to the black hole. We also verify
that the Immirzi field boils down to a constant value in the asymptotic region,
thus restoring the standard loop quantum gravity picture. We finally prove the
violation of the reverse isoperimetric inequality, resulting in the
superentropic nature of the black hole, and we discuss in detail the
thermodynamic stability of the solution.
