  We find a plethora of new analytic black holes and globally regular
horizonless spacetimes in three dimensions. The solutions involve a single real
scalar field $\phi$ which always admits a magnetic-like expression proportional
to the angular coordinate. The new metrics, which satisfy $g_{tt}g_{rr}=-1$ and
represent continuous generalizations of the BTZ one, solve the equations of
Einstein gravity corrected by a new family of densities (controlled by
unconstrained couplings) constructed from positive powers of $(\partial
\phi)^2$ and certain linear combinations of $R^{ab} \partial_a \phi \partial_b
\phi$ and $(\partial \phi)^2 R$. Some of the solutions obtained describe black
holes with one or several horizons. A set of them possesses curvature
singularities, while others have conical or BTZ-like ones. Interestingly, in
some cases the black holes have no singularity at all, being completely
regular. Some of the latter are achieved without any kind of fine tuning or
constraint between the action parameters and/or the physical charges of the
solution. An additional class of solutions describes globally regular and
horizonless geometries.
