  In this paper, we investigate the phase structures of the black holes with
one single higher spin hair, focusing specifically on the spin 3 and spin tilde
4 black holes. Based on dimensional analysis and the requirement of having
consistent thermodynamics, we derive an universal formula relating the entropy
and the conserved charges for arbitrary AdS3 higher spin black holes. Then we
use it to study the phase structure of the higher spin black holes. We find
that there are six branches of solutions in the spin 3 gravity, eight branches
of solutions in the spin tilde 4 gravity and twelve branches of solutions in
the G2 gravity. In each case, all branches are related by a simple angle shift
in the entropy functions. In the spin 3 case, we reproduce all the results
found before. In the spin tilde 4 case, we find that in the low temperature it
is at the BTZ branch while in the high temperature it transits to one of two
other branches, depending on the signature of the chemical potential, a
reflection of charge conjugate asymmetry found before.
