ELMy H-modes are currently a promising scenario envisaged for the operation of a future fusion reactor. The reliable extrapolation of the present experimental data to a reactor requires a model which is capable of explaining the variety of experimental phenomena observed in high-density H-modes. This paper attempts to construct a model based on the assumption that the behaviour of high-density ELMy H-modes can be explained through the similarity of edge transport mechanisms. We have identified three dimensionless parameters as the most representative for the high-density H-mode operation: (a) F = q2R/f(s) representing the ideal ballooning limit, (b) collisionality *e = ZeffnqR/T2e which is postulated to be responsible for the transition from type I to type III edge localized modes (ELMs) and (c) the L-H transition boundary represented by FL-H = T3e/(B2LZeff/(mi)1/2). 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 dependences: e~B/qR for density limits. 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 separatrix density should scale as ne~B/qR, where 1, >1, <1 (but being close to unity) and q is assumed to be the safety factor at 95% of the flux, q95. Good agreement is found between experimental results on JET for the density at the top of the pedestal and the scaling e~B/R3/4q5/4 for the critical separatrix density at the transition, in the conditions where the two densities are expected to be proportional to each other.