We have measured the central structural properties for a sample of S0-Sbc galaxies down to scales of ~10 pc using HST NICMOS images. We find that the photometric masses of the central star clusters, which occur in 58% of our sample, are related to their host bulge masses such that MassPt = 10^{7.75pm0.15}(MassBul/10^{10}MassSun)^{0.76pm 0.13}. Put together with recent data on bulges hosting supermassive black holes, we infer a non-linear dependency of the `Central Massive Object mass on the host bulge mass such that MassCMO = 10^{7.51pm 0.06} (MassBul/10^{10}MassSun)^{0.84 pm 0.06}. We argue that the linear relation presented by Ferrarese et al. is biased at the low-mass end by the inclusion of the disc light from lenticular galaxies in their sample. Matching our NICMOS data with wider-field, ground-based K-band images enabled us to sample from the nucleus to the disk-dominated region of each galaxy, and thus to perform a proper bulge-disk decomposition. We found that the majority of our galaxies (~90%) possess central light excesses which can be modeled with an inner exponential and/or an unresolved point source in the case of the nuclear star clusters. All the extended nuclear components, with sizes of a few hundred pc, have disky isophotes, which suggest that they may be inner disks, rings, or bars; their colors are redder than those of the underlying bulge, arguing against a recent origin for their stellar populations. Surface brightness profiles rise inward to the resolution limit of the data, with a continuous distribution of logarithmic slopes from the low values typical of dwarf ellipticals (0.1 leq gamma leq 0.3) to the high values (gamma ~ 1) typical of intermediate luminosity ellipticals; the nuclear slope bi-modality reported by others is not present in our sample.
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