  We consider metric-affine scenarios where a modified gravitational action is
sourced by electrovacuum fields in a three dimensional space-time. Such
scenarios are supported by the physics of crystalline structures with
microscopic defects and, in particular, those that can be effectively treated
as bi-dimensional (like graphene). We first study the case of $f(R)$ theories,
finding deviations near the center as compared to the solutions of General
Relativity. We then consider Born-Infeld gravity, which has raised a lot of
interest in the last few years regarding its applications in astrophysics and
cosmology, and show that new features always arise at a finite distance from
the center. Several properties of the resulting space-times, in particular in
presence of a cosmological constant term, are discussed.
