The transition reported in L-mode plasmas leading to the formation of a density “shoulder” in the Scrape-off Layer (SOL) of tokamaks is investigated in the three ITER stepladder machines: COMPASS, ASDEX Upgrade (AUG) and JET. In AUG and JET, the broadening of the profiles can be observed at similar relative densities (n_e/n_GW ∼ 0.4–0.5) and coincides with a clear increase in the size of SOL filaments and the onset of the outer divertor detachment. In COMPASS, no transition is observed in the same density range: the divertor does not detach and no clear effect is observed neither in the profiles nor in the turbulence. This is explained as the result of an increase of intermittent transport triggered by the increased resistivity along filaments associated to divertor detachment. The transition conditions in AUG and JET are compared to foreseen ITER SOL parameters, and the implications are briefly discussed.