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.
