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 $\varphi$ which always admits a magneticlike expression proportional to the angular coordinate. The new metrics, which satisfy $g_{tt}{g}_{rr}=-1$ and represent continuous generalizations of the Bañados-Teitelboim-Zanelli (BTZ) one, solve the equations of Einstein gravity corrected by a new family of densities (controlled by unconstrained couplings) constructed from positive powers of $(\partial \varphi {)}^2$ and certain linear combinations of $R^{ab}{\partial }_a\varphi {\partial }_b\varphi$ and $(\partial \varphi {)}^{2}R$. 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.

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• Alternative gravity theories
• Classical black holes
• Gravity in dimensions other than four