We characterise ionised gas outflows using a large sample of ~330 high-luminosity (45.5 < log(L_bol/erg s^-1) < 49.0), high-redshift (1.5 < z < 4.0) quasars via their [OIII]4960,5008 emission. The median velocity width of the [OIII] emission line is 1540 kms^-1, increasing with increasing quasar luminosity. Broad, blue-shifted wings are seen in the [OIII] profiles of 42 per cent of the sample. Rest-frame ultraviolet spectra with well-characterised CIV 1550 emission line properties are available for more than 210 quasars, allowing an investigation of the relationship between the Broad Line Region (BLR) and Narrow Line Region (NLR) emission properties. The [OIII] blueshift is correlated with CIV blueshift, even when the dependence of both quantities on quasar luminosity has been taken into account. A strong anti-correlation between the [OIII] equivalent width (EW) and CIV blueshift also exists. Furthermore, [OIII] is very weak, with EW<1A, in ~10 per cent of the sample, a factor of 10 higher compared to quasars at lower luminosities and redshifts. If the [OIII] emission originates in an extended NLR, the observations suggest that quasar-driven winds are capable of influencing the host-galaxy environment out to kilo-parsec scales. The mean kinetic power of the ionised gas outflows is then 10^44.7 erg s^-1, which is ~0.15 per cent of the bolometric luminosity of the quasar. These outflow efficiencies are broadly consistent with those invoked in current active galactic nuclei feedback models.
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