  We determine radial velocities and mass flow rates in a sample of 54 local
spiral galaxies by modelling high-resolution and high-sensitivity data of the
atomic hydrogen emission line. We found that, although radial inflow motions
seem to be slightly preferred over outflow motions, their magnitude is
generally small. Most galaxies show radial flows of only a few km/s throughout
their HI disks, either inwards or outwards, without any clear increase in
magnitude in the outermost regions, as we would expect for continuous radial
accretion. 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$_\odot$/yr
outside the optical disk and of 0.1 M$_\odot$/yr in the outskirts of the HI
disks. These inflow rates are about 5-10 times smaller than the average star
formation rate of 1.4 M$_\odot$/yr. Our study suggests that there is no clear
evidence for systematic radial accretion inflows that alone could feed and
sustain the star formation process in the inner regions of local spiral
galaxies at its current rate.
