We present new imaging and spectroscopic observations aimed at detecting intervening galaxies responsible for low redshift (z approximately 0.5) Mg II absorption line systems in quasar spectra. New results are reported for 12 absorption systems detected in 10 quasar sightlines. Broad-band imaging in the red with spectroscopic follow-up in 8 cases reveals a spatially resolved object at a redshift equal to that of the Mg II absorption system. The intervening absorbing galaxies typically lie at an angular separation in the range 5" to 12", or a linear distance of 1.5 to 3.5 R(H) (R(H) = 22 kpc with H(o) = 50 km s-1 Mpc-1), and span a moderate magnitude range 19.1 < m(r) < 22.5. Of the four negative cases, two are associated with unreliable Mg II absorption systems. The remaining two include the lowest Mg II redshift of the sample and a 21 cm absorber; on the basis of very deep imaging recently obtained under subarcsec seeing conditions, we suggest that the former is a dwarf galaxy and the latter a galactic disk superimposed onto the quasar image. Our results then appear fully compatible with the intervening galaxy hypothesis and reveal no unsuspected class of absorbers. Our data and those already reported in the literature (with spectroscopic follow-up) are used to build a sample of 17 absorption systems, large enough to start investigating statistical properties. It comprises 13 absorber identifications. The distributions of the absolute r magnitudes and fluxes per unit frequency at lambda-r = 3646 angstrom both only spread over one decade (or 2.5 mag). The absorber average magnitude is M(r) = -21.4. The lack of low-luminosity absorbing galaxies (with the possible exception of one very faint absorber candidate), together with our high detection rate points towards a strong deficiency of low-luminosity galaxies, L < 0.3 L*, with extended gaseous envelopes. In the quasar fields, we also have obtained spectroscopic observations of other galaxies which are used as test sample. The M(r) distribution of the latter covers a large range of 5.5 mag, over twice that for the absorbers, although the spread in apparent magnitudes is somewhat smaller than for the absorbers. These two samples roughly have the same [O II] lambda 3727 rest equivalent width distribution than observed for the z approximately 0.3 field galaxies of the Durham faint galaxy surveys. Consequently, there is no real difference between the increased star formation activity in the past seen in the absorbers and the field galaxy population. To constrain the size and shape of the absorbing regions, we compare the observed distribution of the absorber-quasar projected linear separations to the computed distribution of impact parameters. The two cases investigated are linear and spherical geometries. A highly elongated geometry is ruled out. Spheres, either with a universal radius, R approximately 3.5 R(H), or a radius-luminosity scaling law, R proportional L0.4, are consistent with the data. We reconsider the classical derivation of Mg II halo sizes from absorption line systems statistics, incorporating the most recent results on the local galaxy luminosity function, on the excess of b(j) approximately 22.5 galaxies in the z approximately 0.3 Durham surveys and on the density per unit redshift of Mg II absorption systems as a function of w(r) (Mg II lambda 2796). The minimum value of the radius of the gaseous envelope of an L* galaxy, R*, obtained by assuming that all field galaxies have spherical envelopes, equals R* = 4.2 R(H) if a Schechter luminosity function is adopted. This value is larger than any of the observed linear projected separations. Introducing the evolution in the galaxy counts leads to comparable observed and predicted values for gaseous halo sizes. The implication is that all L > 0.3 L* field galaxies at z approximately 0.4 have extended gaseous envelopes with geometry closer to spheres than to thin disks. Comparison to our Galaxy or local galaxies suggests the presence of a strong evolution from z approximately 0 to 0.5 in halo shapes (or size) and star formation activity.
