  We study the demographics of supermassive black holes (SMBHs) in the local
and high-z universe with hard X-ray luminosity functions (HXLFs) of AGNs.
First, we compare the mass accretion history at z>0 with optical luminosity
functions (OLFs) and that with HXLFs. We consider the constraints on parameters
of mass accretion (energy conversion efficiency and Eddington ratio) and
conclude that the constraints based on HXLFs are more adequate rather than that
based on OLFs. The sub-Eddington case is allowed only when we use HXLFs. Next,
we estimate the upper limit of the cumulative mass density of SMBHs at any
redshifts. For an application, we examine if Lyman-Break galaxies (LBGs) at z=3
already have SMBHs in their centers which is suggested by recent observations.
If most of LBGs already has massive SMBHs at z=3, the resultant mass density of
SMBHs at z=0 should exceed the observational estimate because such SMBHs should
further grow by accretion. We show that the special conditions should be met in
order that a large part of LBGs have SMBHs (for example, large energy
conversion efficiency and frequent mergers and/or direct formations at z>3).
The possibility that nearly all LBGs have SMBHs with large mass ratio, such as
M_BH/M_stellar > 0.005, is reliably ruled out.(abridged)
