  We investigate the implications of the current data regarding large scale
anisotropies, and examine to what extent they can be used to constrain the
origin of UHECRs and the astrophysical parameters of the source scenarios. We
discuss the possibility of observing an associated anisotropy of the
composition, the potential benefit of the separation of the different nuclear
components and the interest of observing the UHECR sky with larger exposure
future observatories. We simulate UHECR sky maps for various astrophysical
scenarios satisfying the current observational constraints, taking into account
the energy losses of the UHE protons and nuclei and their deflections by
intervening magnetic fields. We investigate scenarios in which the UHECR source
distribution follows that of the galaxies, varying the source composition and
spectrum, the source density and the magnetic field models. We apply similar
analyses as those used by the Auger collaboration. We find that: i) reproducing
the observed dipole anisotropy and its energy evolution is relatively easy
within our assumptions; ii) this agreement can be obtained with different sets
of assumptions on the astrophysical parameters, and is thus not, at this stage,
very constraining for UHECR source scenarios; iii) the actual reconstructed
direction of the dipole appears non natural in essentially all scenarios
investigated, and challenges their main assumptions on the source distribution
or the assumed magnetic field configuration, especially in the Galaxy; iv)
except for protons, the energy range in which the GZK horizon strongly reduces
is a key target for anisotropy searches for each given nuclear species; v) The
composition anisotropy naturally expected in our models is unlikely to account
for that recently reported by Auger unless the observed amplitude is a strong
positive statistical fluctuation of an intrinsically weaker signal.
