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Cool gas (T$\sim$10$^{4}$~K) traced by hydrogen Ly$\alpha$ emission is now routinely detected around $z\sim3$ quasars, but little is known about their molecular gas reservoirs. Here, we present an APEX spectroscopic survey of the CO(6-5), CO(7-6) and [CI](2-1) emission lines for 9 quasars from the QSO MUSEUM survey which have similar UV luminosities, but very diverse Ly$\alpha$ nebulae. These observations ($\langle~\rm rms~\rangle=2.6$~mJy in 300~km~s$^{-1}$) detected three CO(6-5) lines with 3.4$\leq I_{\rm CO(6-5)} \leq$5.1~Jy~km~s$^{-1}$, 620$\leq$FWHM$\leq$707~km~s$^{-1}$, and three [CI](2-1) lines with 2.3$\leq I_{\rm [CI](2-1)} \leq$15.7~Jy~km~s$^{-1}$, 329$\leq$FWHM$\leq$943~km~s$^{-1}$. For the CO and [CI] detected sources, we constrain the molecular gas reservoirs to be $\rm M_{H_{2}} = (0.4-6.9) \times 10^{11} M_{\odot}$, while the non-detections imply $\rm M_{H_{2}} < 1.1\times 10^{11} M_{\odot}$. We compare our observations with the extended Ly$\alpha$ properties to understand the link between the cool and the molecular gas phases. We find large velocity shifts between the bulk of Ly$\alpha$ and the molecular gas systemic redshift in five sources (from $\sim$-400 to $\sim+$1200~km~s$^{-1}$). The sources with the largest shifts have the largest Ly$\alpha$ line widths in the sample, suggesting more turbulent gas conditions and/or large-scale inflows/outflows around these quasars. We also find that the brightest ($I_{\rm[CI](2-1)}=15.7\pm3.7~\rm Jy~km~s^{-1}$) and the widest (FWHM$\sim$900~km~s$^{-1}$) lines are detected for the smallest and dimmest Ly$\alpha$ nebulae. From this, we speculate that host galaxy obscuration can play an important role in reducing the ionizing and Ly$\alpha$ photons able to escape to halo scales, and/or that these systems are hosted by more massive halos., Comment: Accepted on January 3, MNRAS. 25 pages, 17 figures

We investigate the radio properties of a sample of 53 sources selected at 850 $��$m from the SCUBA-2 Cosmology Legacy Survey using new deep, low-frequency radio imaging of the Lockman Hole field from the Low Frequency Array. Combining these data with additional radio observations from the GMRT and the JVLA, we find a variety of radio spectral shapes and luminosities within our sample despite their similarly bright submillimetre flux densities. We characterise their spectral shapes in terms of multi-band radio spectral indices. Finding strong spectral flattening at low frequencies in ~20% of sources, we investigate the differences between sources with extremely flat low-frequency spectra and those with `normal' radio spectral indices. As there are no other statistically significant differences between the two subgroups of our sample as split by the radio spectral index, we suggest that any differences are undetectable in galaxy-averaged properties that we can observe with our unresolved images, and likely relate to galaxy properties that we cannot resolve, on scales $\lesssim$ 1 kpc. We attribute the observed spectral flattening in the radio to free-free absorption, proposing that those sources with significant low-frequency spectral flattening have a clumpy distribution of star-forming gas. We estimate an average spatial extent of absorbing material of at most several hundred parsecs to produce the levels of absorption observed in the radio spectra. This estimate is consistent with the highest-resolution observations of submillimetre galaxies in the literature, which find examples of non-uniform dust distributions on scales of ~100 pc, with evidence for clumps and knots in the interstellar medium. Additionally, we find two bright (> 6 mJy) submm sources undetected at all other wavelengths. We speculate that these objects may be very high redshift sources, likely residing at z > 4., 15 pages, 10 figures, accepted by A&A