The extrapolability of present plasma scenarios to ITER partly depends on whether the same shape of the density profile will be realized also in burning plasmas. The shape of the density profile has important consequences on both the plasma confinement and the plasma stability. In a burning plasma, with the same temperature profiles and the same volume averaged density, a peaked density profile produces larger amount of fusion power and bootstrap current with respect to a at profile. On the other hand, a too peaked density profile might have negative consequences on both the MHD stability and central accumulation of heavy impurities. Recent experimental results in AUG and JET H-mode plasmas indicate that the density peaking is correlated with the plasma collisionality. This observation might lead to the prediction that density profiles in the ITER standard scenario will not be at, as usually assumed, but peaked, since ITER collisionality is expected to be as low as the lowest collisionalities achieved in present devices. However, as long as results from a single device are considered, collisionality is correlated with other plasma parameters, in particular the Greenwald fraction, the normalized ion Larmor radius r* and the fuelling provided by the beams. For the first time, here we present an empirical scaling for the density peaking taking into account observations from more than one device. We show that by combining observations from different devices, while some correlations are indeed reduced, also additional uncertainties are introduced. The way we have adopted to overcome the limitations encountered is discussed. Multiple regression analyses are performed which confirm that in the combined database of AUG and JET observations, collisionality is the most relevant parameter in the regressions. Scalings for density peaking are proposed and ITER projections are discussed.