Regular black holes in three dimensions

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