  We analytically investigate backreaction by a quantum scalar field on two
rotating Ba\~nados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole
and that of a naked singularity. In the former case, we explore the quantum
effects on various regions of relevance for a rotating black hole space-time.
We find that the quantum effects lead to a growth of both the event horizon and
the radius of the ergosphere, and to a reduction of the angular velocity,
compared to the unperturbed values. Furthermore, they give rise to the
formation of a curvature singularity at the Cauchy horizon and show no evidence
of the appearance of a superradiant instability. In the case of a naked
singularity, we find that quantum effects lead to the formation of a horizon
that shields it, thus supporting evidence for the r\^ole of quantum mechanics
as a cosmic censor in nature.
