  We revisit the study of (A)dS black holes in Lovelock theories. We present a
new tool that allows to attack this problem in full generality. In analyzing
maximally symmetric Lovelock black holes with non-planar horizon topologies
many distinctive and interesting features are observed. Among them, the
existence of maximally symmetric vacua do not supporting black holes in vast
regions of the space of gravitational couplings, multi-horizon black holes, and
branches of solutions that suggest the existence of a rich diagram of phase
transitions. The appearance of naked singularities seems unavoidable in some
cases, raising the question about the fate of the cosmic censorship conjecture
in these theories. There is a preferred branch of solutions for planar black
holes, as well as non-planar black holes with high enough mass or temperature.
Our study clarifies the role of all branches of solutions, including
asymptotically dS black holes, and whether they should be considered when
studying these theories in the context of AdS/CFT.
