  (Abridged) Recent results from the Pierre Auger Observatory (PAO) indicate
that the composition of ultra-high-energy cosmic rays (UHECRs) with energies
above $10^{19}$ eV may be dominated by heavy nuclei. An important question is
whether the distribution of arrival directions for such UHECR nuclei can
exhibit observable anisotropy or positional correlations with their
astrophysical source objects despite the expected strong deflections by
intervening magnetic fields. For this purpose, we have simulated the
propagation of UHECR nuclei including models for both the extragalactic
magnetic field and the Galactic magnetic field. Assuming that only iron nuclei
are injected steadily from sources with equal luminosity and spatially
distributed according to the observed large scale structure in the local
Universe, at the number of events published by the PAO so far, the arrival
distribution of UHECRs would be consistent with no auto-correlation at 95%
confidence if the mean number density of UHECR sources $n_s >~ 10^{-6}$
Mpc$^{-3}$, and consistent with no cross-correlation with sources within 95%
errors for $n_s >~ 10^{-5}$ Mpc$^{-3}$. On the other hand, with 1000 events
above $5.5 \times 10^{19}$ eV in the whole sky, next generation experiments can
reveal auto-correlation with more than 99% probability even for $n_s <~
10^{-3}$ Mpc$^{-3}$, and cross-correlation with sources with more than 99%
probability for $n_s <~ 10^{-4}$ Mpc$^{-3}$. In addition, we find that the
contribution of Centaurus A is required to reproduce the currently observed
UHECR excess in the Centaurus region. Secondary protons generated by
photodisintegration of primary heavy nuclei during propagation play a crucial
role in all cases, and the resulting anisotropy at small angular scales should
provide a strong hint of the source location if the maximum energies of the
heavy nuclei are sufficiently high.
