Kerr black holes without primary hairs

We present a class of regular axisymmetric black hole geometries fully characterized by the parameters $\{\mathcal{M},a\}$ and possessing the Kerr event horizon. This family interpolates between regular spacetimes, configurations with integrable singularities, and the Kerr solution as a limiting case. Its main features are: (i) the existence of quasi-extremal configurations without requiring $a\approx \mathcal{M}$; and (ii) a possible framework toward an analytical description of Kerr black hole formation from an initially regular configuration.