  We present imaging of the HI 21cm absorption line system seen toward the
nuclear regions of Mrk 231 at z = 0.04217, and imaging of the radio continuum
emission at 1.4 GHz, on scales ranging from a few parsecs to a few hundred
parsecs. These data indicate the existence of a sub-kpc gas disk in Mrk 231, as
seen in HI 21cm absorption and in radio continuum emission. The radio continuum
morphology is consistent with a disk of maximum radius of 440 mas, at an
inclination angle of 45deg, with a major axis oriented east-west. The HI 21cm
absorption shows an east-west gradient in position and velocity of about +/-110
km/s out to radii of 100 mas. We identify this HI and radio continuum disk as
the inner part of the molecular disk seen on a factor three larger scale. The
physical conditions for the thermal and non-thermal gas in the sub-kpc disk of
Mrk 231 are similar to those proposed for compact nuclear starburst galaxies,
and in particular to the conditions proposed for the sub-kpc gas disk in Arp
220. From the neutral hydrogen velocity field we derive a gravitational mass
enclosed within a 50 pc radius of 3x10**8 solar masses. We derive a massive
star formation rate in the disk of 60 solar masses per year. We also present a
search for HI 21cm absorption associated with the optical broad absorption line
systems toward Mrk 231. We do not detect HI 21cm absorption associated with any
of the optical BAL systems. These negative results require that the neutral
atomic gas in the BAL clouds be fairly warm (T > 50 K), unless the NaI
abundance is higher than solar, or the dust-to-gas ratio is higher than
Galactic, or the observed extinction toward the nucleus of Mrk 231 is not due
to the BAL gas.
