Results from an extensive profile database analysis of JET density profiles in H-mode show that the density peaking factor n(e0)/ < n(e) > in JET H-modes increases as the effective collisionality v(eff) congruent to 10(-14) RZ(eff)n(e)/T-e(2) drops from similar to 1 at mid-radius to below 0.1 as expected for ITER. Density peaking is also strongly correlated with the Greenwald number N-G, the particle outward flux Gamma from the neutral beam source and T-i/T-e. The correlations with l(i), q(95), beta(N), rho*, L-Te, L-Ti, the toroidal Mach number and its shear are weak or insignificant. H-modes heated only by ICRH are, on average, only slightly less peaked than H-modes dominated by NBI, demonstrating that neutral beam fuelling can only explain a modest part (similar to 20%) of the peaking. Scaling expressions involving v(eff), N-G, R Gamma/(n(e)chi) and T-i/T-e suggest that n(e0)/ < n > may exceed 1.5 in ITER, providing a boost of fusion power of more than 30% for fixed beta and average density with respect to the usual assumption of a flat density profile.