  We model the galactic discs of seven nearby large spiral galaxies as
three-component systems consist of stars, molecular gas, and atomic gas in
vertical hydrostatic equilibrium. We set up the corresponding joint
Poisson-Boltzmann equation and solve it numerically to estimate the
three-dimensional distribution of HI in these galaxies. While solving the
Poisson-Boltzmann equation, we do not consider a constant HI velocity
dispersion ($\sigma_{\rm HI}$); rather, we develop an iterative method to
self-consistently estimate the $\sigma_{\rm HI}$ profile in a galaxy by using
the observed second-moment profile of the HI spectral cube. Using the density
solutions, we determine the HI vertical scale height in our galaxies. We find
that the HI discs flare in a linear fashion as a function of radius. HI scale
height in our galaxies is found to vary between a few hundred parsecs at the
center to $\sim 1-2$ kpc at the outskirts. We estimate the axial ratio of the
HI discs in our sample galaxies and find a median ratio of 0.1, which is much
lower than what is found for dwarf galaxies, indicating much thinner HI discs
in spiral galaxies. Very low axial ratios in three of our sample galaxies (NGC
5055, NGC 6946, and NGC 7331) suggest them to be potential superthin galaxies.
Using the HI distribution and the HI hole sizes in NGC 6946, we find that most
of the HI holes in this galaxy are broken out into the circumgalactic medium
and this breaking out is more effective in the inner radii as compared to the
outer radii.
