  We present structural measurements for the galaxies in the 0.05<z<0.0585
groups of the Zurich Environmental Study, aimed at establishing how galaxy
properties depend on four environmental parameters: group halo mass M_GROUP,
group-centric distance R/R_200, ranking into central or satellite, and
large-scale structure density delta_LSS. Global galaxy structure is quantified
both parametrically and non-parametrically. We correct all these measurements
for observational biases due to PSF blurring and surface brightness effects as
a function of galaxy size, magnitude, steepness of light profile and
ellipticity. Structural parameters are derived also for bulges, disks and bars.
We use the galaxy bulge-to-total ratios (B/T), together with the calibrated
non-parametric structural estimators, to implement a quantitative morphological
classification that maximizes purity in the resulting morphological samples. We
investigate how the concentration C of satellite galaxies depends on galaxy
mass for each Hubble type, and on M_GROUP, R/R_200 and delta_LSS. At galaxy
masses M>10^10 M_sun, the concentration of disk satellites increases with
increasing stellar mass, separately within each morphological bin of B/T. The
known increase in concentration with stellar mass for disk satellites is thus
due, at least in part, to an increase in galaxy central stellar density at
constant B/T. The correlation between concentration and galaxy stellar mass
becomes progressively steeper for later morphological types. The concentration
of disk satellites shows a barely significant dependence on delta_LSS or
R/R_200. The strongest environmental effect is found with group mass for
M>10^10 M_sun disk-dominated satellites, which are ~10% more concentrated in
high mass groups than in lower mass groups.
