  The star formation rate (SFR) and black hole accretion rate (BHAR) functions
are measured to be proportional to each other at z < ~3. This close
correspondence between SF and BHA would naturally yield a BH mass-galaxy mass
correlation, whereas a BH mass-bulge mass correlation is observed. To explore
this apparent contradiction we study the SF in spheroid-dominated galaxies
between z=1 and the present day. We use 903 galaxies from the COMBO-17 survey
with M* >2x10^10M_sun, ultraviolet and infrared-derived SFRs from Spitzer and
GALEX, and morphologies from GEMS HST/ACS imaging. Using stacking techniques,
we find that <25% of all SF occurs in spheroid-dominated galaxies (Sersic index
n>2.5), while the BHAR that we would expect if the global scalings held is
three times higher. This rules out the simplest picture of co-evolution, in
which SF and BHA trace each other at all times. These results could be
explained if SF and BHA occur in the same events, but offset in time, for
example at different stages of a merger event. However, one would then expect
to see the corresponding star formation activity in early-stage mergers, in
conflict with observations. We conclude that the major episodes of SF and BHA
occur in different events, with the bulk of SF happening in isolated disks and
most BHA occurring in major mergers. The apparent global co-evolution results
from the regulation of the BH growth by the potential well of the galactic
spheroid, which includes a major contribution from disrupted disk stars.
