  Galaxies in the local Universe are thought to require ongoing replenishment
of their gas reservoir in order to maintain the observed star formation rates.
Cosmological simulations predict that such accretion can occur in both a
dynamically hot and cold mode. However, until now observational evidence of the
accretion required to match the observed star formation histories is lacking.
This paper attempts to determine whether galaxies in the local Universe possess
a significant reservoir of HI and what would be the accretion rates derived
from such reservoirs. We search the vicinity of 22 nearby galaxies for isolated
HI clouds or distinct streams in a systematic and automated manner. The HALOGAS
observations represent one of the most sensitive and detailed HI surveys to
date. These observations typically reach column density sensitivities of 10^19
cm^-2 over a 20 km/s width. We find 14 secure HI cloud candidates without an
observed optical counterpart. These cloud candidates appear to be analogues to
the most massive clouds detected around the Milky Way and M31. However, on
average their numbers seem significantly reduced. We constrain upper limits for
HI accretion in the local Universe. The average HI mass currently observed
amounts to a rate of 0.05 Msun/yr with a stringent upper limit of 0.22 Msun/yr,
confirming previous estimates. This is much lower than the average star
formation rate in this sample. Our best estimate, based on GBT detection limits
of several galaxies, suggests that another 0.04 Msun/yr could be accreted from
undetected clouds and streams. These results show that in nearby galaxies HI is
not being accreted at the same rate as stars are currently being formed. Our
study can not exclude that other forms of gas accretion are at work. However,
these observations also do not reveal extended neutral gas reservoirs around
most nearby spiral galaxies.
