We report the results of 3D simulations of non-diffusive propagation o
f Ultra High Energy Cosmic Rays (UHECR) (E >10(20) eV) through the int
ergalactic and extended halo media. We quantify the expected angular a
nd temporal correlations between the events and the sources, and the t
emporal delay between protons and gamma-ray counterparts with a common
origin for both halo and extragalactic origins. It is shown that the
proposed UHECR-supergalactic plane source associations require either
extremely high values of the halo magnetic field over as much as 100 k
pc length scale or a very large correlation length for the IGM, even f
or the largest possible values of the intergalactic magnetic field. It
can be stated that the UHECR seem to point to the sources even more s
trongly than previously believed. The simulations also show that the c
alculated time delays between UHE protons and gamma-ray counterparts d
o not match the claimed GRB-UHECR associations for either cosmological
or extended halo distance scales. (C) 1997 Elsevier Science B.V.