Abstract. In the second half of the 90s interest grew on the complex features of the magnetospheric dynamics in response to solar wind changes. An important series of papers were published on the occurrence of chaos, turbulence and complexity. Among them, particularly interesting was the study of the bursty and fractal/multifractal character of the high latitude energy release during geomagnetic storms, which was evidenced by analyzing the features of the Auroral Electrojet (AE) indices. Recently, the multifractal features of the small time-scale increments of AE-indices have been criticized in favor of a more simple fractal behavior. This is particularly true for the scaling features of the probability density functions (PDFs) of the AE index increments. Here, after a brief review of the nature of the fractal/multifractal features of the magnetospheric response to solar wind changes, we investigate the multifractal nature of the scaling features of the AE index increments PDFs using the Rank Ordering Multifractal Analysis (ROMA) technique. The ROMA results clearly demonstrate the existence of a hierarchy of scaling indices, depending on the increment amplitude, for the data collapsing of PDFs relative to increments at different time scales. Our results confirm the previous results by Consolini et al. (1996) and the more recent results by Rypdal and Rypdal (2010).