Black hole and nuclear cluster scaling relations: M_bh ~
  M_nc^{2.7+/-0.7}
  There is a growing array of supermassive black hole and nuclear star cluster
scaling relations with their host spheroid, including a bent (black hole
mass)-(host spheroid mass) M_bh-M_sph relation and different (massive compact
object mass)-(host spheroid velocity dispersion) M_mco-sigma relations for
black holes and nuclear star clusters. By combining the observed M_bh ~
sigma^(5.5) relation with the observed M_nc ~ sigma^(1.6--2.7) relation, we
derive the expression M_bh ~ (M_nc)^(2--3.4), which should hold until the
nuclear star clusters are eventually destroyed in the larger core-Sersic
spheroids. This new mass scaling relation helps better quantify the rapid
evolutionary growth of massive black holes in dense star clusters, and the
relation is consistently recovered when coupling the observed M_nc ~
(M_sph)^(0.6--1.0) relation with the recently observed quadratic relation M_bh
~ (M_sph)^2 for Sersic spheroids.
