Astrophysical and space plasmas are commonly found to be out of thermal equilibrium i.e., the velocity distribution functions of their particles are not well described by Maxwellian distributions. They generally have more suprathermal particles in the tail of the distribution. The kappa distribution provides a generalization to successfully describe such plasmas with tails decreasing as a power law of the velocity. In the present work, we improve the solar wind model developed on the basis of such kappa distributions by incorporating azimuthally varying 1 AU boundary conditions to produce a spatially structured view of the solar wind expansion. By starting from the top of the chromosphere to the heliosphere and by applying relevant boundary conditions in the ecliptic plane, a global model of the corona and the solar wind is developed for each particle species. The model includes the natural heating of the solar corona automatically appearing when an enhanced population of suprathermal particles is present at low altitude in the solar (or stellar) atmosphere. This applies not only for electrons and protons but also for the minor ions which then have a temperature increase proportional to their mass. Moreover, the presence of suprathermal electrons contributes to the acceleration of the solar wind to high bulk velocities when Coulomb collisions are neglected. The results of the model are illustrated in the solar corona and in solar wind for the different particle species and can now be directly compared in two dimensions with spacecraft observations in the ecliptic plane. Key Points Kappa distributions successfully describe plasmas out of thermal equilibrium A global kinetic model of the solar corona and solar wind is described The model is extended by incorporating azimuthally varying boundary conditions.