We present a general formulation for the analysis of cool clouds co-rotating around a star which permits us to construct so-called visibility plots which limit the clouds' heights and latitudes. We apply this formalism to the case of neutral hydrogen clouds in the rapidly rotating late-type stars, HK Aqr and AB Dor. We argue that these clouds are most likely confined to equatorial regions and that they exist at a variety of heights above the stellar photosphere, ranging from a few percent of a stellar radius to a few stellar radii. We argue, as a result that the 'coronal condensation' model of Cameron and Robinson (1989a,b), invoking cloud formation at the co-rotation radius, does not apply to these objects. Based on stability arguements we show that it is unlikely that the clouds are filament-like structures. As an alternative we consider the possibility that the clouds are part of large coronal loop-like structures possessing temperature inversions. The temperature inversion is likely to be caused by a decrease of the coronal heating at large distances from the star and by the increase of the cross-section towards the apex. We discuss the possibility of Doppler imaging of clouds and show that this is in general not possible because of the properties of the kernel of the integral equation which needs to be solved. The typical lifetimes of clouds are estimated to be of the order of days.