  We summarize the main features of a class of \emph{asymptotically anomalous}
(asymptotically flat, but non Schwarzschild-like) gravitational configurations
in models of gravitating non-linear electrodynamics in three space dimensions,
whose Lagrangian densities are defined as arbitrary functions of the two field
invariants and constrained by several physical admissibility conditions. This
class of models and their associated electrostatic spherically symmetric black
hole solutions are characterized by the behaviours of the Lagrangian densities
around the vacuum and at the boundary of their domain of definition.
