  Analysing the available data relative to the anisotropies of the
ultra-high-energy cosmic rays (UHECR) at intermediate angular scales, we
examine to what extent they can be used to constrain the origin of these
particles, and what could be gained from a new generation of observatories with
increased exposure. We simulate realistic UHECR sky maps for a wide range of
scenarios, with the assumption that the distribution of UHECR sources follows
that of matter in the Universe, also considering possible biases. We produce
numerous datasets on which we apply similar analyses as those recently used by
the Auger and TA collaborations. We find that: i) the investigated scenarios
can easily account for the significance of the anisotropies reported by Auger
and TA; ii) the direction in which the maximum flux excess is found in the
Auger data differs from where it is found in most of our simulations; iii) for
datasets simulated with the same astrophysical scenario, the significance with
which the isotropy hypothesis is rejected through the Auger likelihood analysis
can be largest either when "all galaxies" or when "starburst" galaxies are used
to model the signal, depending on which GMF model is used; iv) the study of the
energy evolution of the anisotropy patterns can provide new insight about the
origin of UHECRs; v) the direction in which the most significant flux excess is
found in the Auger dataset above 8 EeV appears to essentially disappear in the
dataset above 32 EeV; vi) this appears to be very uncommon in our simulations,
which could point to a failure of some generic assumption in the investigated
scenarios, such as the predominance of a unique type of sources in the flux
above the ankle, with essentially the same composition and spectrum; vii) a
meaningful measurement of their energy evolution, from 10 EeV to the highest
energies, will require a significant increase in statistics.
