  We present single-dish CO(1-0) and CO(2-1) observations for 14 low-redshift
quasi-stellar objects (QSOs). In combination with optical integral field
spectroscopy we study how the cold gas content relates to the star formation
rate (SFR) and black hole accretion rate. CO(1-0) is detected in 8 of 14
targets and CO(2-1) is detected in 7 out of 11 cases. The majority of
disc-dominated QSOs reveal gas fractions and depletion times well matching
normal star forming systems. Two gas-rich major mergers show clear starburst
signatures with higher than average gas fractions and shorter depletion times.
Bulge-dominated QSO hosts are mainly undetected in CO(1-0) which corresponds,
on average, to lower gas fractions than in disc-dominated counterparts. Their
SFRs however imply shorter than average depletion times and higher star
formation efficiencies. Negative QSO feedback through removal of cold gas seems
to play a negligible role in our sample. We find a trend between black hole
accretion rate and total molecular gas content for disc-dominated QSOs when
combined with literature samples. We interpret this as an upper envelope for
nuclear activity which is well represented by a scaling relation between the
total and circum-nuclear gas reservoir accessible for accretion.
Bulge-dominated QSOs significantly differ from that scaling relation and appear
uncorrelated with the total molecular gas content. This could be explained
either by a more compact gas reservoir, blow out of the gas envelope through
outflows, or a different ISM phase composition.
