  A four-dimensional regularization of Lovelock-Lanczos gravity up to an
arbitrary curvature order is considered. We show that Lovelock-Lanczos terms
can provide a non-trivial contribution to the Einstein field equations in four
dimensions, for spherically symmetric and
Friedmann-Lema\^{i}tre-Robertson-Walker spacetimes, as well as at first order
in perturbation theory around (anti) de Sitter vacua. We will discuss the
cosmological and black hole solutions arising from these theories, focusing on
the presence of attractors and their stability. Although curvature
singularities persist for any finite number of Lovelock terms, it is shown that
they disappear in the non-perturbative limit of a theory with a unique vacuum.

General Relativity and Quantum Cosmology;High Energy Physics - Theory