Abstract
The Mallett model of a charged, rotating, evaporating black hole in an inflationary universe is examined. The structure and location of the timelike limit surfaces, apparent horizons, and event horizons are determined. It is noted that a coupling between the cosmological constant and the angular momentum of the black hole produces an axially symmetric deformation of the event horizons which is not seen in noninflationary models. The cosmic censorship conjecture is considered for this model. It is demonstrated that the inflation-rotation coupling can lead to quasinaked primordial singularities in the latter stages of inflation. Such singularities are visible from equatorial regions, but not visible from polar regions.