  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 $2.5
\times 10^{20} eV$) propagating through the galactic magnetic field from the
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.
