  Ultra High Energy (UHE) neutrino Astronomy and relic Neutrino masses may play
a key role in solving the Ultra High Energy Cosmic Ray (UHECR) puzzle within
the Z-Showering model. Tau air-shower originated by UHE neutrino in matter may
probe and amplify this expected UHE neutrino Astronomy. The discover of
upcoming and horizontal tau air-showers (UPTAUs, HORTAUs), born by UHE, nu_tau
interacting inside mount chains or along Earth Crust crown masses at the
Horizons edges, will greatly amplify the single UHE nu_tau track. Observing
UPTAUs and HORTAUs along their line of showering, from higher balloons or
satellites, at Greisen-Zatsepin-Kuzmin (GZK) energies above 10^19 eV, may test
a calorimeter mass exceeding 150 km^3 (water equivalent). Observing Horizontal
Shower by EUSO will probe even larger ring areas generated in huge terrestrial
volumes larger than 2360 km^3. These highest GZK energies nu_tau astronomy are
well tuned to test the needed abundant nu fluence in GZK Z-Showering model
where ZeV (above 10^21 eV) Ultra High Energy neutrinos hit on relic light (near
0.1-3 eV masses) anti-neutrinos, in hot dark matter halos, creating boosted UHE
Z bosons. Their nucleon decay in flight may born secondaries observed on Earth
atmosphere as UHECR. The wide EUSO acceptance may test easily Z-showering
fluxes as well as GZK neutrinos at their minimal granted fluence. The rare (78)
observed upcoming terrestrial gamma flashes observed by BATSE satellite during
last decade may be also be traces of such UPTAUs and HORTAUs.
