The peakedness of density profiles in L-modes and in H-modes exhibits remarkably different behaviour. The former scales with overall plasma shear in accordance with Turbulent EquiPartition (TEP) theory (ne0 /<ne>~1.5li), independently of collisionality. On the other hand, peaking in H-modes depends on collisionality, with ne0 /<ne> increasing from ~1.2 at veff = 1 to ne0 /<ne> ~1.6 at the collisionality of the ITER reference H-mode, veff 0.1. H-mode density profiles show no shear dependence, except for veff <0.2. Evidence for LTe, LTi or r* dependences has been obtained neither in L nor in H-modes. Carbon density profiles from CXS are always less peaked than electron density profiles.