  We use a semi-analytic galaxy formation model to study the co-evolution of
supermassive black holes (SMBHs) with their host galaxies. Although the
coalescence of SMBHs is not important, the quasar-mode accretion induced by
mergers plays a dominant role in the growth of SMBHs. Mergers play a more
important role in the growth of SMBH host galaxies than in the SMBH growth. It
is the combined contribution from quasar mode accretion and mergers to the SMBH
growth and the combined contribution from starburst and mergers to their host
galaxy growth that determine the observed scaling relation between the SMBH
masses and their host galaxy masses. We also find that mergers are more
important in the growth of SMBH host galaxies compared to normal galaxies which
share the same stellar mass range as the SMBH host galaxies.
