| Summary: | We report the results of 3D simulations of the trajectories of ultra-high energy protons and Fe nuclei (with energies $E = 4 \times 10^{19}$ and $2.5 sources to the detector. A uniform distribution of anti-particles is backtracked from the detector, at the Earth, to the halo of the Galaxy. We assume an axisymmetric, large scale spiral magnetic field permeating both the disc and the halo. A normal field component to the galactic plane ($B_z$) is also included in part of the simulations. We find that the presence of a large scale galactic magnetic field does not generally affect the arrival directions of the protons, although the inclusion of a $B_z$ component may cause significant deflection of the lower energy protons ($E = 4 \times 10^{19} $ eV). Error boxes larger than or equal to $\sim 5^{\circ}$ are most expected in this case. On the other hand, in the case of heavy nuclei, the arrival direction of the particles is strongly dependent on the coordinates of the particle source. The deflection may be high enough ($> 20^{\circ}$) as to make extremely difficult any identification of the sources unless the real magnetic field configuration is accurately determined. Moreover, not every incoming particle direction is allowed between a given source and the detector. This generates sky patches which are virtually unobservable from the Earth. In the particular case of the UHE events of Yakutsk, Fly's Eye, and Akeno, they come from locations for which the deflection caused by the assumed magnetic field is not significant.
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