  In the present work we study the scale dependence at the level of the
effective action of charged black holes in Einstein-Maxwell as well as in
Einstein-power-Maxwell theories in (2+1)-dimensional spacetimes without a
cosmological constant. We allow for scale dependence of the gravitational and
electromagnetic couplings, and we solve the corresponding generalized field
equations imposing the "null energy condition". Certain properties, such as
horizon structure and thermodynamics, are discussed in detail.
