  The hierarchical build-up of galactic bulges should lead to the build-up of
present-day supermassive black holes by a mixture of gas accretion and merging
of supermassive black holes. The tight relation between black hole mass and
stellar velocity dispersion is thereby a strong argument that the supermassive
black holes in merging galactic bulges do indeed merge. Otherwise the ejection
of supermassive black holes by gravitational slingshot would lead to excessive
scatter in this relation. At high redshift the coalescence of massive black
hole binaries is likely to be driven by the accretion of gas in the major
mergers signposted by optically bright QSO activity. If massive black holes
only form efficiently by direct collapse of gas in deep galactic potential
wells with v_c > 100 km/s as postulated in the model of Kauffmann & Haehnelt
(2000) LISA expects to see event rates from the merging of massive binary black
holes of about 0.1-1 yr^{-1} spread over the redshift range 0 < z < 5. If,
however, the hierarchical build-up of supermassive black holes extends to
pre-galactic structures with significantly shallower potential wells event
rates may be as high as 10-100 yr^{-1} and will be dominated by events from
redshift z > 5.
