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Direct Ly $\alpha$ imaging of intergalactic gas at $z\sim2$ has recentlyrevealed giant cosmological structures around quasars, e.g. the Slug Nebula(Cantalupo et al. 2014). Despite their high luminosity, the detection rate ofsuch systems in narrow-band and spectroscopic surveys is less than 10%,possibly encoding crucial information on the distribution of gas around quasarsand the quasar emission properties. In this study, we use the MUSEintegral-field instrument to perform a blind survey for giant Ly $\alpha$nebulae around 17 bright radio-quiet quasars at $3<z<4$ that does not sufferfrom most of the limitations of previous surveys. After data reduction andanalysis performed with specifically developed tools, we found that each quasaris surrounded by giant Ly $\alpha$ nebulae with projected sizes larger than 100physical kpc and, in some cases, extending up to 320 kpc. The circularlyaveraged surface brightness profiles of the nebulae appear very similar to eachother despite their different morphologies and are consistent with power lawswith slopes $\approx-1.8$. The similarity between the properties of all thesenebulae and the Slug Nebula suggests a similar origin for all systems and thata large fraction of gas around bright quasars could be in a relatively "cold"(T$\sim$10$^4$K) and dense phase. In addition, our results imply that such gasis ubiquitous within at least 50 kpc from bright quasars at $3<z<4$independently of the quasar emission opening angle, or extending up to 200 kpcfor quasar isotropic emission.

Ubiquitous giant Ly $\alpha$ nebulae around the brightest quasars at $z\sim3.5$ revealed with MUSE