  Models and observations suggest that both power and effects of AGN feedback
should be maximised in hyper-luminous (L_Bol>10^47 erg/s) quasars, i.e. objects
at the brightest end of the AGN luminosity function. We present the first
results of a multi-wavelength observing program, focusing on a sample of
WISE/SDSS selected hyper-luminous (WISSH) broad-line quasars at z~1.5-5. The
WISSH quasars project has been designed to reveal the most energetic AGN-driven
outflows, estimate their occurrence at the peak of quasar activity and extend
the study of correlations between outflows and nuclear properties up to
poorly-investigated extreme AGN luminosities (L_Bol~10^47 -10^48 erg/s). We
present NIR, long-slit LBT/LUCI1 spectroscopy of five WISSH quasars at
z~2.3-3.5 showing prominent [OIII] emission lines with broad (FWHM~1200-2200
km/s) and skewed profiles. The luminosities of the broad [OIII] wings are the
highest measured so far (L_[OIII]^broad >~5x10^44 erg/s) and reveal the
presence of powerful ionised outflows with mass outflow rates Mdot >~1700
M_Sun/yr and kinetic powers Edot >~10^45 erg/s. Although these estimates are
affected by large uncertainties, due to the use of [OIII] as tracer of ionized
outflows and the very basic outflow model we assume, these results suggest that
the AGN is highly efficient in pushing outwards large amounts of ionised gas in
our targets. The mechanical outflow luminosities for WISSH quasars correspond
to higher fractions (~1-3%) of L_Bol than those derived for lower L_Bol AGN.
Our targets host very massive (M_BH>~2x10^9 M_Sun) black holes which are still
accreting at a high rate (i.e. a factor of ~0.4-3 of the Eddington limit).
These findings demonstrate that WISSH quasars offer the opportunity of probing
the extreme end of both luminosity and SMBH mass functions and revealing
powerful ionised outflows able to affect the evolution of their host galaxies.
