  Photometrically distinct nuclear star clusters (NSCs) are common in
late-type-disk and spheroidal galaxies. The formation of NSCs is inevitable in
the context of normal star formation in which a majority of stars form in
clusters. A young, mass-losing cluster embedded in an isolated star-forming
galaxy remains gravitationally bound over a period determined by its initial
mass and the galactic tidal field. The cluster migrates radially toward the
center of the galaxy and becomes integrated in the NSC if it reaches the
center. The rate at which the NSC grows by accreting young clusters can be
estimated from empirical cluster formation rates and dissolution times. We
model cluster migration and dissolution and find that the NSCs in late-type
disks and in spheroidals could have assembled from migrating clusters. The
resulting stellar nucleus contains a small fraction of the stellar mass of the
galaxy; this fraction is sensitive to the high-mass truncation of the initial
cluster mass function (ICMF). The resulting NSC masses are consistent with the
observed values, but generically, the final NSCs are surrounded by a spatially
more extended excess over the inward-extrapolated exponential (or Sersic) law
of the outer galaxy. We suggest that the excess can be related to the
pseudobulge phenomenon in disks, though not all of the pseudobulge mass
assembles this way. Comparison with observed NSC masses can be used to
constrain the truncation mass scale of the ICMF and the fraction of clusters
suffering prompt dissolution. We infer truncation mass scales of <~ 10^6 M_sun
(>~ 10^5 M_sun) without (with 90%) prompt dissolution.
