Ion measurements made by the Phobos 2 spacecraft revealed an extensive, ever-persisting escape of planetary ions in the Martian tail. Observations indicated that in large regions of the Martian tail, most ions were of planetary origin. The measurements suggested that the solar wind pickup of planetary ions is an important factor in the global Mars-solar wind interaction. However, how in detail the newly formed planetary ions affect the formation of the observed global plasma and field regions remained unanswered. In this paper the escape of Martian ions is studied with a quasi-neutral hybrid simulation model. The used hybrid model includes two ion species: the solar wind protons and the planetary ions. This approach makes it possible to study the asymmetries associated with the finite ion gyroradius as well as the difference between the motion of the solar wind protons and planetary ions. The source of the escaping ions is studied indirectly by producing planetary ions from two ion sources: the neutral corona (photoionization) and the ionosphere. The simulation is found to reproduce many observed features of the Mars-solar wind interaction in general and those of the planetary ions in particular. Ion escape within the optical shadow forms an antisunward flowing beam of ~1 keV planetary ions, much as observed. A total mass loss rate of ~100--400 g s-1 is found to be large enough to reproduce several plasma and magnetic field features observed by Phobos2 on its circular orbits. Simulations produce a wide region behind the planet where the density and the particle flux of H+ ions are much smaller than their solar wind values, resembling the observed proton cavity. The work also depicts how the ionotail, formed mainly by the escaping planetary ions, is embedded in the Martian magnetotail. The runs also result in a notable asymmetry with respect to the direction of the convectice electric field in the solar wind which is caused by the finite ion gyroradius. The magnetopause also demonstrates the asymmetry: the magnetopause is a sharp boundary or a smooth transition layer, depending on the direction of the upstream convective electric field. Overall, the work illustrates the importance of the plasma-neutral interactions in the global Mars-solar wind interaction.