We compare the gas distribution, kinematics and the current star formation in
a sample of 10 very faint (-13.37 < M_B < -9.55) dwarf galaxies. For 5 of these
galaxies we present fresh, high sensitivity, GMRT HI 21cm observations. For all
our galaxies we construct maps of the HI column density at a constant linear
resolution of ~300 pc; this forms an excellent data set to check for the
presence of a threshold column density for star formation. We find that while
current star formation (as traced by Halpha emission) is confined to regions
with relatively large (N_HI > (0.4 -1.7) X 10^{21} atoms cm^{-2}) HI column
density, the morphology of the Halpha emission is in general not correlated
with that of the high HI column density gas. Thus, while high column density
gas may be necessary for star formation, in this sample at least, it is not
sufficient to ensure that star formation does in fact occur. We examine the
line profiles of the HI emission, but do not find a simple relation between
regions with complex line profiles and those with on-going star formation.
Finally, we examine the very fine scale (~20-100 pc) distribution of the HI
gas, and find that at these scales the emission exhibits a variety of shell
like, clumpy and filamentary features. The Halpha emission is sometimes
associated with high density HI clumps, sometimes the Halpha emission lies
inside a high density shell, and sometimes there is no correspondence between
the Halpha emission and the HI clumps. In summary, the interplay between star
formation and gas density in these galaxy does not seem to show the simple
large scale patterns observed in brighter galaxies (abridged).Comment: 15 pages, 6 tables, 13 figures. Accepted for publication in MNRA