  We present 12CO (J=1-0) observations of a sample of local galaxies
(0.04<z<0.08) with a large neutral hydrogen reservoir, or "HI monsters". The
data were obtained using the Redshift Search Receiver on the FCRAO 14 m
telescope. The sample consists of 20 HI-massive galaxies with M(HI)>3e10Msun
from the ALFALFA survey and 8 LSBs with a comparable M(HI) (>1.5e10Msun). Our
sample selection is purely based on the amount of neutral hydrogen, thereby
providing a chance to study how atomic and molecular gas relate to each other
in these HI-massive systems. We have detected CO in 15 out of 20 ALFALFA
selected galaxies and 4 out of 8 LSBs with molecular gas mass M(H2) of
(1-11)e9Msun. Their total cold gas masses of (2-7e10Msun make them some of the
most gas-massive galaxies identified to date in the Local Universe. Observed
trends associated with HI, H2, and stellar properties of the HI massive
galaxies and the field comparison sample are analyzed in the context of
theoretical models of galaxy cold gas content and evolution, and the importance
of total gas content and improved recipes for handling spatially differentiated
behaviors of disk and halo gas are identified as potential areas of improvement
for the modeling.
