We have compared kinetic and fluid model descriptions of the proton polar wind outflow, from the collision-dominated, subsonic regime at lower altitudes, through the transition to supersonic flow, and well into the supersonic flow regime. The kinetic model is based on the Fokker-Planck collision operator, and the two fluid models employed are based on the 8-moment expansion and the 16-moment bi-Maxwellian expansions, respectively. We find excellent agreement between the kinetic description and the fluid models for the proton density and flux, even in the transonic and supersonic flow regimes. The models are also in qualitative agreement for the temperature and heat flux moments, although neither fluid model reproduces the negative (downward) kinetic heat fluxes found at high altitudes. The 16-moment fluid model gives a temperature anisotropy similar to the anisotropy derived from the kinetic solution. The assumed forms for the velocity distribution, on which the fluid expansions are based, do not agree with the kinetic velocity distribution, except in the subsonic region where the departure from a Maxwellian distribution is small. Near the fluid critical point the kinetic model develops a double-hump distribution, with an isotropic, low-energy core and an anisotropic, high-energy tail, and at higher altitudes the distribution function develops a kidney bean shape. ¿ 1998 American Geophysical Union