We determine radial velocities and mass flow rates in a sample of 54 localspiral galaxies by modelling high-resolution and high-sensitivity data of theatomic hydrogen emission line. We found that, although radial inflow motionsseem to be slightly preferred over outflow motions, their magnitude isgenerally small. Most galaxies show radial flows of only a few km/s throughouttheir HI disks, either inwards or outwards, without any clear increase inmagnitude in the outermost regions, as we would expect for continuous radialaccretion. Gas mass flow rates for most galaxies are less than 1 M$_\odot$/yr.Over the entire sample, we estimated an average inflow rate of 0.3 M$_\odot$/yroutside the optical disk and of 0.1 M$_\odot$/yr in the outskirts of the HIdisks. These inflow rates are about 5-10 times smaller than the average starformation rate of 1.4 M$_\odot$/yr. Our study suggests that there is no clearevidence for systematic radial accretion inflows that alone could feed andsustain the star formation process in the inner regions of local spiralgalaxies at its current rate.

We investigate the dark matter halos of 256 star-forming disc-like galaxiesat $z\sim 1$ using the KMOS redshift one spectroscopic survey (KROSS). Thissample covers the redshifts $0.6 \leq z \leq 1.04$, effective radii $0.69 \leqR_e [\mathrm{kpc}] \leq 7.76$, and total stellar masses $8.7 \leqlog(M_{\mathrm{star}} \ [\mathrm{M_\odot}]) \leq 11.32$. We present a massmodelling approach to study the rotation curves of these galaxies, which allowus to dynamically calculate the physical properties associated with the baryonsand the dark matter halo. For the former we assume a Freeman disc, while forthe latter we employ the NFW and the Burkert halo profiles, separately. At theend, we compare the results of both cases with state-of-the-art cosmologicalgalaxy simulations (EAGLE, TNG100 and TNG50). We find that the {\em cored} darkmatter halo emerged as the dominant quantity from a radius 1-3 times theeffective radius. Its fraction to the total mass is in good agreement with theoutcome of hydrodynamical galaxy simulations. Remarkably, we found that thedark matter core of $z\sim 1$ star-forming galaxies are smaller and denser thantheir local counterparts. We conclude that dark matter halos have graduallyexpanded over the past 6.5 Gyrs. That is, observations are capable of capturingthe dark matter response to the baryonic processes (e.g. feedbacks), and thusgiving us the first empirical evidence of {\em gravitational potentialfluctuations} in the inner region of galaxies, which can be verified with deepsurveys and future missions.