The flow of gas into and out of galaxies leaves traces in the circumgalactic medium which can then be studied using absorption lines towards background quasars. We analyse 27 log[N(H I) /cm(-2)] > 18. 0 H I absorbers at z = 0.2 to 1.4 from the MUSEALMA Haloes survey with at least one galaxy counterpart within a line of sight velocity of +/- 500 km s(-1). We perform 3D kinematic forward modelling of these associated galaxies to examine the flow of dense, neutral gas in the circumgalactic medium. From the VLT/MUSE, HST broad-band imaging, and VLT/UVES and Keck/HIRES high-resolution UV quasar spectroscopy observations, we compare the impact parameters, star-formation rates, and stellar masses of the associated galaxies with the absorber properties. We find marginal evidence for a bimodal distribution in azimuthal angles for strong H I absorbers, similar to previous studies of the Mg II and O VI absorption lines. There is no clear metallicity dependence on azimuthal angle, and we suggest a larger sample of absorbers is required to fully test the relationship predicted by cosmological hydrodynamical simulations. A case-by-case study of the absorbers reveals that ten per cent of absorbers are consistent with gas accretion, up to 30 per cent trace outflows, and the remainder trace gas in the galaxy disc, the intragroup medium, and low-mass galaxies below the MUSE detection limit. Our results highlight that the baryon cycle directly affects the dense neutral gas required for star-formation and plays a critical role in galaxy evolution.