Central Structural Parameters of Early-Type Galaxies as Viewed with Nicmos on the [ITAL]HUBBLE SPACE TELESCOPE[/ITAL][ITAL]Hubble Space Telescope[/ITAL]

We present surface photometry for the central regions of a sample of 33 early-type (E, S0, and S0/a) galaxies observed at 1.6 microns (H band) using the Hubble Space Telescope (HST). We employ a new technique of two-dimensional fitting to extract quantitative parameters for the bulge light distribution and nuclear point sources, taking into consideration the effects of the point-spread function. Parameterizing the bulge profile with a ``Nuker'' law, we confirm that the central surface-brightness distributions largely fall into two categories, each of which correlates with the global properties of the galaxies. ``Core'' galaxies tend to be luminous ellipticals with boxy or pure elliptical isophotes, whereas ``power-law'' galaxies are preferentially lower luminosity systems with disky isophotes. Unlike most previous studies, however, we do not find a clear gap in the distribution of inner cusp slopes; several objects have inner cusp slopes (0.3 < gamma < 0.5) which straddle the regimes conventionally defined for core and power-law type galaxies. The nature of these intermediate objects is unclear. We draw attention to two objects in the sample which appear to be promising cases of galaxies with isothermal cores that are not the brightest members of a cluster. Unresolved nuclear point sources are found in about 50% of the sample galaxies, roughly independent of profile type, with magnitudes in the range m^{nuc}_H = 12.8 to 17.4 mag, which correspond to M_H^{nuc} = -12.8 to -18.4 mag. (Abridged)