  We present near-infrared H-band (1.65micron) observations and surface
brightness profile decompositions for 75 faint (13.5 < m_p < 18.5) galaxies,
primarily taken among dwarf Ellipticals members of the Virgo cluster. We model
their surface brightness profiles with a de Vaucouleurs (D), exponential (E),
mixed (bulge+disk or M) or truncated (T) law, and we derive for each galaxy the
H band effective surface brightness (mu_e) and effective radius (r_e), the
asymptotic total magnitude H_T and the light concentration index C_31.
Combining the present data with those previously obtained by our group (1157
objects) we analyze the NIR properties of a nearly complete sample,
representative of galaxies of all morphological types, spanning 4 decades in
luminosity. We confirm our earlier claim that the presence of cusps and
extended haloes in the light profiles (C_31>5) is a strong, non-linear function
of the total luminosity. We also find that: i) among dEs and dS0s galaxies D
profiles are absent; 50% of the decompositions are of type M, the remaining
being of type E or T. ii) Less than 50% of the giant elliptical galaxies have
pure D profiles, the majority being represented by M profiles. iii) Most giant
galaxies (from elliptical to Sb) have M profiles. iv) Most of late type spirals
(Scd to BCD) have either E or T profiles. v) The type of decomposition is a
strong function of the total H band luminosity, independent of the Hubble
classification: the fraction of type E decompositions decreases with increasing
luminosity, while those of type M increase with luminosity. Pure D profiles are
absent in the low luminosity range L_H<10^10 solar and become dominant above
10^11 solar, while T profiles are present only among low luminosity galaxies.
