This paper presents a model of precipitated fluxes from the PSBL and CPS. Simulation results and data from Aureol-3 spacecraft indicate the presence of velocity dispersed precipitated ion structures (VDIS) at the poleward edge of the auroral oval. These structures are associated with fast ion beams in the PSBL region of the Earth's magnetotail, confirming previous experimental results. The simulations also reveal possible substructuring of the VDIS. The bulk of the PSBL population which is not precipitated is very effectively thermalized and quasi-isotropized after multiple interactions with the magnetotail current layer. After each reflection cycle some part of the distribution is precipitated and forms multiple 'echoes' of VDIS. The CPS distributions occurring as a result of scattering, convection, multiple reflections and Fermi acceleration appear isotropic in the simulation model. This paper portrays the important role of the VDIS auroral region medium for complicated and energetically significant processes occurring in different regions of the distant magnetotail. ¿ American Geophysical Union 1992