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We present a study of the environment of 27 z=3-4.5 bright quasars from theMUSE Analysis of Gas around Galaxies (MAGG) survey. With medium-depth MUSEobservations (4 hours on target per field), we characterise the effects ofquasars on their surroundings by studying simultaneously the properties ofextended gas nebulae and Lyalpha emitters (LAEs) in the quasar host haloes. Wedetect extended (up to ~ 100 kpc) Lyalpha emission around all MAGG quasars,finding a very weak redshift evolution between z=3 and z=6. By stacking theMUSE datacubes, we confidently detect extended emission of CIV and onlymarginally detect extended HeII up to ~40 kpc, implying that the gas is metalenriched. Moreover, our observations show a significant overdensity of LAEswithin 300 km/s from the quasar systemic redshifts estimated from the nebularemission. The luminosity functions and equivalent width distributions of theseLAEs show similar shapes with respect to LAEs away from quasars suggesting thatthe Lyalpha emission of the majority of these sources is not significantlyboosted by the quasar radiation or other processes related to the quasarenvironment. Within this framework, the observed LAE overdensities and ourkinematic measurements imply that bright quasars at z=3-4.5 are hosted byhaloes in the mass range ~ 10^{12.0}-10^{12.5} Msun.

MUSE Analysis of Gas around Galaxies (MAGG) -- III: The gas and galaxy environment of z = 3-4.5 quasars