  The tensor virial theorem for subsystems is formulated for three-component
systems and further effort is devoted to a special case where the inner
subsystems and the central region of the outer one are homogeneous, the last
surrounded by an isothermal homeoid. The virial equations are explicitly
written under additional restrictions. An application is made to hole + vortex
+ bulge systems, in the limit of flattened inner subsystems. Using the
Faber-Jackson relation, the standard $M_{\rm H}$-$\sigma_0$ form is deduced
from qualitative considerations. The projected bulge velocity dispersion to
projected vortex velocity ratio, $\eta$, as a function of the fractional
radius, y_{\rm BV}, and the fractional masses, $m_{\rm BH}$, and $m_{\rm VH}$,
is plotted for several cases. It is shown that a fixed value of $\eta$ below
the maximum corresponds to two different configurations: a compact bulge on the
left and an extended bulge on the right. In addition, for fixed $m_{\rm BH}$ or
$m_{\rm BV}$, and $y_{\rm BV}$, more massive bulges are related to larger
$\eta$ and vice versa. The model is applied to NGC 4374 and NGC 4486, and the
bulge mass is inferred and compared with results from different methods. In
presence of a massive vortex $(m_{\rm VH}=5)$, the hole mass has to be reduced
by a factor 2-3 with respect to the case of a massless vortex, to get the fit.
