  The Arecibo Legacy Fast ALFA (ALFALFA) survey is designed to explore the z=0
HI mass function (HIMF) over a cosmologically significant volume. ALFALFA will
improve on previous determinations of the HIMF by its combination of depth,
wide area and centroiding accuracy, the latter allowing, in most cases,
immediate identification of the optical counterpart to each HI signal. ALFALFA
will detect hundreds of galaxies with HI masses less than 10**7.5 solar masses
and also greater than 10**10.5 solar masses, and its final catalog will allow
investigation of the dependence of the HIMF both on local density and on galaxy
morphology. Already ALFALFA confirms previous suggestions that there is no
cosmologically significant population of HI-rich dark galaxies. Fewer than 3%
of all extragalactic HI sources and < 1% of ones with HI masses > 10**9.5 solar
masses cannot be identified with a stellar counterpart. Very preliminary
results on the presence of gas-rich dwarfs in the void in front of the
Pisces-Perseus supercluster suggest an underabundance of such objects compared
to the predictions of numerical simulations. The objects with highest HI mass
exhibit a range of morphologies and optical colors and surface brightnesses but
all appear to be massive disk systems. The latter represent the population
likely to dominate future studies of HI at higher redshift with the Square
Kilometer Array.
