ELMy H-modes are currently the main scenario envisaged for ITER operation. The reliable extrapolation of present experimental data to ITER requires a model which is capable of explaining the variety of experimental phenomena observed in high density H-modes. In particular, it has to provide correct scalings for the main operational points identified on the edge ne – Te - operational diagram. In all tokamaks, the maximum density was found to scale approximately as ne ~B/qR in agreement with the Greenwald/Hugill scaling. The present paper is an attempt to construct such a model with the assumption that behaviour of high density ELMy H-modes can be explained through the similarity of edge transport mechanisms. Three dimensionless parameters have been identified as the most representative for the high density H-mode operation: a) Fβ = q2R∇β/ƒ(s) representing the ideal ballooning limit, b) ν* = ZeffnqR/Te2 collisionality which is postulated to be responsible for the transition from type I to type III ELMs and c) the L-H transition boundary represented by FL–H = Te3/(B2L⊥Zeff/√mi). Fixing any two out of these three parameters allows one to find scalings for the main operational points in the edge ne – Te diagram and reproduce the Greenwald/Hugill dependencies. More detailed scalings for the type I to type III ELM transition point, which may be of particular interest for a reactor, show that the critical edge density should scale as ne ~ Bα/qβRγ, where α≈1, β>1 and γ<1 (but being close to unity). One particular scaling for the critical edge density (near or at the separatrix) consistent with the ne ~ B/q5/4 collisional skin-depth model was found to be in a good agreement with results of a dedicated series of experiments on JET which confirmed the dependence for the line average density. The scaling for ne,crit, however, was found to be not very sensitive to the transport model selected and other models yielded very similar dependencies.