We report the detection of extended Lyα haloes around 145 individual star-forming galaxies at redshifts 3 ≤ z ≤ 6 in the Hubble Ultra Deep Field observed with the Multi-Unit Spectroscopic Explorer (MUSE) at ESO-VLT. Our sample consists of continuum-faint (− 15 ≥ MUV ≥ −22) Lyα emitters (LAEs). Using a 2D, two-component (continuum-like and halo) decomposition of Lyα emission assuming circular exponential distributions, we measure scale lengths and luminosities of Lyα haloes. We find that 80% of our objects having reliable Lyα halo measurements show Lyα emission that is significantly more extended than the UV continuum detected by HST (by a factor ≈4 to >20). The median exponential scale length of the Lyα haloes in our sample is ≈4.5 kpc with a few haloes exceeding 10 kpc. By comparing the maximal detected extent of the Lyα emission with the predicted dark matter halo virial radii of simulated galaxies, we show that the detected Lyα emission of our selected sample of Lyα emitters probes a significant portion of the cold circum-galactic medium of these galaxies (>50% in average). This result therefore shows that there must be significant HI reservoirs in the circum-galactic medium and reinforces the idea that Lyα haloes are ubiquitous around high-redshift Lyα emitting galaxies. Our characterization of the Lyα haloes indicates that the majority of the Lyα flux comes from the halo (≈65%) and that their scale lengths seem to be linked to the UV properties of the galaxies (sizes and magnitudes). We do not observe a significant Lyα halo size evolution with redshift, although our sample for z> 5 is very small. We also explore the diversity of the Lyα line profiles in our sample and we find that the Lyα lines cover a large range of full width at half maximum (FWHM) from 118 to 512 km s-1. While the FWHM does not seem to be correlated to the Lyα scale length, most compact Lyα haloes and those that are not detected with high significance tend to have narrower Lyα profiles (<350 km s-1). Finally, we investigate the origin of the extended Lyα emission but we conclude that our data do not allow us to disentangle the possible processes, i.e. scattering from star-forming regions, fluorescence, cooling radiation from cold gas accretion, and emission from satellite galaxies.