  The distribution of stars and gas in many galaxies is asymmetric. This
so-called lopsidedness is expected to significantly affect the dynamics and
evolution of the disc, including the star formation activity. Here, we measure
the degree of lopsidedness for the gas distribution in a selected sample of 70
galaxies from the Westerbork HI Survey of Spiral and Irregular Galaxies. This
complements our earlier work (Paper I) where the kinematic lopsidedness was
derived for the same galaxies. The morphological lopsidedness is measured by
performing a harmonic decomposition of the surface density maps. The amplitude
of lopsidedness A_1, the fractional value of the first Fourier component, is
typically quite high (about 0.1) within the optical disc and has a constant
phase. Thus, lopsidedness is a common feature in galaxies and indicates a
global mode. We measure A_1 out to typically one to four optical radii,
sometimes even further. This is, on average, four times larger than the
distance to which lopsidedness was measured in the past using near-IR as a
tracer for the old stellar component, and will therefore provide a new, more
stringent constraint on the mechanism for the origin of lopsidedness.
Interestingly, the value of A_1 saturates beyond the optical radius.
Furthermore, the plot of A_1 vs. radius shows fluctuations which we argue are
due to local spiral features. We also try to explain the physical origin of
this observed disc lopsidedness. No clear trend is found when the degree of
lopsidedness is compared to a measure of the isolation or interaction
probability of the sample galaxies. However, this does not rule out a tidal
origin if the lopsidedness is long-lived. Additionally, we find that the
early-type galaxies tend to be more morphologically lopsided than late-type
galaxies. Both results together indicate a tidal origin for the lopsidedness.
