  (Abridged) We study the nuclear star clusters in spiral galaxies of various
Hubble types using spectra obtained with STIS on-board HST. We observed the
nuclear clusters in 40 galaxies, selected from two previous HST/WFPC2 imaging
surveys. The spectra provide a better separation of cluster light from
underlying galaxy light than is possible with ground-based spectra. To infer
the star formation history, metallicity and dust extinction, we fit weighted
superpositions of single-age stellar population templates to the spectra. The
luminosity-weighted age ranges from 10 Myrs to 10 Gyrs. The stellar populations
of NCs are generally best fit as a mixture of populations of different ages.
This indicates that NCs did not form in a single event, but instead they had
additional star formation long after the oldest stars formed. On average, the
sample clusters in late-type spirals have a younger luminosity-weighted mean
age than those in early-type spirals (log(age/yr) = 8.37+/-0.25 vs.
9.23+/-0.21). The average cluster masses are smaller in late-type spirals than
in early-type spirals (log(M/Msun) = 6.25+/-0.21 vs. 7.63+/-0.24), and exceed
the masses typical of globular clusters. The cluster mass correlates strongly
with both the Hubble type of the host galaxy and the luminosity of its bulge.
The latter correlation has the same slope as the well-known correlation between
supermassive black hole mass and bulge luminosity. The properties of both
nuclear clusters and black holes are therefore intimately connected to the
properties of the host galaxy.
