We use observations from the Ulysses electron spectrometer to examine global trends of the electron suprathermal population and to study, for the first time, the electron core, halo, and total temperature gradients in the fast solar wind over the poles. We use a data set covering the period from the beginning of the mission (1990, day of year 322) to approximately the first completion of Ulysses out-of-ecliptic orbit around the Sun (1998, day 32). This allows us to characterize very well the two states of the solar wind: the high-speed wind, emanating from polar coronal holes, and the low-speed streams, emanating from equatorial regions. From a classical bi-Maxwellian (core and halo) model of electron velocity distribution functions, we define the electron suprathermal strengths S as the ratio of the halo to core kinetic pressures: S=nhTh/ncTc. The fast wind has larger average values of S than the slow wind. This global correlation between S and the solar wind bulk speed is also observed on a smaller scale in the polar regions. We find that the small-scale variations of the solar wind bulk speed in the polar regions, typically ¿50 km/s around an average value of 750 km/s, are correlated with small-scale variations of S. We present also the first observations of the electron core, halo, and total temperature gradients in time-stationary fast solar wind periods over the poles. We examine all the previous observations in the context of simple solar wind exospheric models. We find, for instance, that the total electron temperature can be well fitted by a law of the form Te=T0+T1r-4/3, as predicted by the exospheric approximation. ¿ 2000 American Geophysical Union