  We consider the propagation of ultra high energy cosmic rays through
turbulent magnetic fields and study the transition between the regimes of
single and multiple images of point-like sources. The transition occurs at
energies around $E_c\simeq Z~41 {\rm EeV}(B_{rms}/5 \mu{\rm G}) (L/ 2 {\rm
kpc})^{3/2}\sqrt{50 {\rm pc}/L_c}$, where $L$ is the distance traversed by the
CR's with electric charge $Ze$ in the turbulent magnetic field of root mean
square strength $B_{rms}$ and coherence length $L_c$. We find that above $2
E_c$ only sources located in a fraction of a few % of the sky can reach large
amplifications of its principal image or start developing multiple images. New
images appear in pairs with huge magnifications, and they remain amplified over
a significant range of energies. At decreasing energies the fraction of the sky
in which sources can develop multiple images increases, reaching about 50% for
$E>E_c/2$. The magnification peaks become however increasingly narrower and for
$E<E_c/3$ their integrated effect becomes less noticeable. If a uniform
magnetic field component is also present it would further narrow down the
peaks, shrinking the energy range in which they can be relevant. Below $E\simeq
E_c/10$ some kind of scintillation regime is reached, where many demagnified
images of a source are present but with overall total magnification of order
unity. We also search for lensing signatures in the AGASA data studying
two-dimensional correlations in angle and energy and find some interesting
hints.
