  Rotating black holes in Einstein-Maxwell-Chern-Simons theory possess
remarkable features, when the Chern-Simons coupling constant reaches a critical
value. Representing single asymptotically flat black holes with horizons of
spherical topology, they exhibit non-uniqueness. In particular, there even
exist extremal and non-extremal black holes with the same sets of global
charges. Both extremal and non-extremal black holes form sequences of radially
excited solutions, that can be labeled by the node number of the magnetic gauge
potential function. The extremal Reissner-Nordstr\"om solution is no longer
always located on the boundary of the domain of existence of these black holes,
and it neither remains the single extremal solution with vanishing angular
momentum. Instead a whole sequence of rotating extremal $J=0$ solutions is
present, whose mass converges towards the mass of the Reissner-Nordstr\"om
solution. These radially excited extremal solutions are all associated with the
same near horizon solution. Moreover, there are near horizon solutions that are
not realized as global solutions.

General Relativity and Quantum Cosmology