  We study the gravitational lensing magnification produced by the intervening
cosmological matter distribution, as deduced from three different hierarchical
models (SCDM, LCDM, CHDM) on very high redshift sources, particularly
supernovae in protogalactic (Pop III) objects. By means of ray-shooting
numerical simulations we find that caustics are more intense and concentrated
in SCDM models. The magnification probability function presents a moderate
degree of evolution up to $z\approx 5$ (CHDM) and $z\approx 7$ (SCDM/LCDM). All
models predict that statistically large magnifications, $\mu \simgt 20$ are
achievable, with a probability of the order of a fraction of percent, the SCDM
model being the most efficient magnifier. All cosmologies predict that above
$z\approx 4$ there is a 10% chance to get magnifications larger than 3. We have
explored the observational perspectives for Pop III SNe detection with NGST
when gravitational magnification is taken into account. We find that NGST
should be able to detect and confirm spectroscopically Type II SNe up to a
redshift of $z \approx 4$ in the J band (for $T_{SN}=25000$ K); this limit
could be increased up to $z\approx 9$ in the K band, allowing for a relatively
moderate magnification. Possibly promising strategies to discriminate among
cosmological models using their GL magnification predictions and very high-$z$
SNe are sketched. Finally, we outline and discuss the limitations of our study.
