  We investigate the relation between star formation rates ($\dot{M}_{s}$) and
AGN properties in optically selected type 1 quasars at $2<z<3$ using data from
Herschel and the SDSS. We find that $\dot{\rm{M}}_s$ remains approximately
constant with redshift, at $300\pm100~\rm{M}_{\odot}$yr$^{-1}$. Conversely,
$\dot{\rm{M}}_s$ increases with AGN luminosity, up to a maximum of
$\sim600~\rm{M}_{\odot}$yr$^{-1}$, and with CIV FWHM. In context with previous
results, this is consistent with a relation between $\dot{\rm{M}}_s$ and black
hole accretion rate ($\dot{\rm{M}}_{bh}$) existing in only parts of the
$z-\dot{\rm{M}}_{s}-\dot{\rm{M}}_{bh}$ plane, dependent on the free gas
fraction, the trigger for activity, and the processes that may quench star
formation. The relations between $\dot{\rm{M}}_s$ and both AGN luminosity and
CIV FWHM are consistent with star formation rates in quasars scaling with black
hole mass, though we cannot rule out a separate relation with black hole
accretion rate. Star formation rates are observed to decline with increasing
CIV equivalent width. This decline can be partially explained via the Baldwin
effect, but may have an additional contribution from one or more of three
factors; $M_i$ is not a linear tracer of L$_{2500}$, the Baldwin effect changes
form at high AGN luminosities, and high CIV EW values signpost a change in the
relation between $\dot{\rm{M}}_s$ and $\dot{\rm{M}}_{bh}$. Finally, there is no
strong relation between $\dot{\rm{M}}_s$ and Eddington ratio, or the asymmetry
of the CIV line. The former suggests that star formation rates do not scale
with how efficiently the black hole is accreting, while the latter is
consistent with CIV asymmetries arising from orientation effects.
