  We investigate the nature of objects in a complete sample of 28 galaxies
selected from the first sky area fully covered by ALFALFA, being well-detected
and having HI profiles wider than 550 km/s. The selection does not use
brightness, morphology, or any other property derived from optical or other
spectral bands. We investigate the degree of isolation, the morphology, and
other properties gathered or derived from open data bases and show that some
objects have wide HI profiles probably because they are disturbed or are
interacting, or might be confused in the ALFALFA beam. We identify a sub-sample
of 14 galaxies lacking immediate interacting neighbours and showing regular,
symmetric, two-horned HI profiles that we propose as candidate high-mass disk
systems (CHMDs).
  We measure the net-Halpha emission from the CHMDs and combine this with
public multispectral data to model the global star formation (SF) properties of
each galaxy. The Halpha observations show SFRs not higher than a few solar
masses per year. Simple SF models indicate that the CHMDs formed most of their
stars almost a Hubble time ago, but most also underwent an SF event in the last
1-10 Myrs; the young stars now produce 10 to 30% of the visible light. The
spatial distribution of the SF-regions is compatible with recycled stellar
ejecta.
  We calculate representative dynamical masses from 1 to $\sim7 10^{11}$ M_sun,
larger by factors of 2.5 to 7.5 than the baryonic masses of the luminous stars
and gas. We test the Tully-Fisher relation for the CHMDs and show that these
lie below the relation defined for lower mass galaxies, i.e., that their M_dyn
is lower than expected when extrapolating the relation from lower mass galaxies
to higher HI line widths.
