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We discuss the generic properties of a general, smoothly varying, sphericallysymmetric mass distribution $\mathcal{D}(r,\theta)$, with no cosmological term($\theta$ is a length scale parameter). Observing these constraints, we showthat (a) the de Sitter behavior of spacetime at the origin is generic anddepends only on $\mathcal{D}(0,\theta)$, (b) the geometry may posses up to$2(k+1)$ horizons depending solely on the total mass $M$ if the cumulativedistribution of $\mathcal{D}(r,\theta)$ has $2k+1$ inflection points, and (c)no scalar invariant nor a thermodynamic entity diverges. We define newtwo-parameter mathematical distributions mimicking Gaussian and step-likefunctions and reduce to the Dirac distribution in the limit of vanishingparameter $\theta$. We use these distributions to derive in closed formsasymptotically flat, spherically symmetric, solutions that describe and model avariety of physical and geometric entities ranging from noncommutative blackholes, quantum-corrected black holes to stars and dark matter halos for variousscaling values of $\theta$. We show that the mass-to-radius ratio $\pi c^2/G$is an upper limit for regular-black-hole formation. Core--multi-shell andmulti-shell regular black holes are also derived.

Smoothed one-core and core--multi-shell regular black holes