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.
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