Sunspots are restricted to a latitude band within 30degof the solar equator. In contrast, the latitudes of spots on the surfaces of rapidly rotating cool stars can range from their polar regions, for RS CVn systems and for T Tauri stars leaving the Hayashi track, to mid latitudes for stars close to or on the main sequence. In order to find an explanation for these observed spot latitudes we have applied the criteria for the undulatory instability (Parker instability) of a toroidal magnetic flux tube embedded in the convective overshoot layer below the outer convection zone and calculated the non-linear evolution of the rising magnetic loops formed by this instability. We describe the results for a star of one solar mass in different phases of its evolution before and on the main sequence. We find that there usually is a range of latitudes at which magnetic flux can emerge on the stellar surface. The mean latitude of emergence shifts towards the poles for increasingly rapid rotation. The internal structure of the star, however, plays an almost equally important role in determining the latitude of magnetic emergence. For stars of solar mass only the youngest objects, with extremely deep convection zones, should show spots emerging at the stellar poles. Pre-main sequence stars at an age of 10^7^ y (convection zone reaching down half-way to the centre) exhibit high latitude, but not truly polar spots, while a main sequence star of one solar mass, even at high rotation rates, only shows intermediate latitude spots. These results are found to be in good agreement with Doppler images of young rapid rotators.