  Quasars trace the most massive structures at high redshifts and their
presence may influence the evolution of the massive host galaxies. We study the
extended Lyman alpha emission line regions (EELRs) around seven bright, mostly
radio-quiet quasars (QSOs) at 2.7<z<4.5, and compare luminosities with EELRs
around radio-loud QSOs reported in the literature. Using integral field
spectroscopy, we analyse the morphology and kinematics of the quiescent Lya
EELRs around the QSOs. We find evidence for the presence of EELRs around four
radio-quiet and one radio-loud QSO. All EELRs appear asymmetric and the
optically brightest QSOs also have the brightest Lya nebulae. For the two
brightest nebulae we find velocities between ~600 km s^-1 at the QSO position
to ~200 km s^-1 at a distance of 3-4 arcsec from the QSO and surface flux
densities up to 2-3*10^{-16} erg cm^-2 s^-1 arcsec^-2. The five EELRs have
total Lya luminosities which correspond to ~0.5% of the luminosities from the
QSOs broad Lya emission lines. This fraction is an order of magnitude smaller
than found for EELRs around radio-loud, steep spectrum QSOs reported in the
literature. While the nebulae luminosities are correlated with the QSO Lya
luminosities, we find that nebulae luminosities are not correlated with the
central QSO ionising fluxes. The presence of gas in the EELRs can be
interpreted based on two competing scenarios: either from quasar feedback
mechanisms, or from infalling matter. Apart from these two effects, the Lya
flux around radio-loud objects can be enhanced due to interactions with the
radio jets. The relatively fainter nebulae around radio-quiet QSOs compared to
lobe-dominated radio-loud QSOs can be ascribed to this effect, or to
significant differences in the environments between the two classes.
