Resumen
In Downarow icz and Lacroix (2006 Law of series) and Downarowicz et al (2007 ESAIM P&S), the authors show that for every ergodic aperiodic dynamical system, the process generated by a typical partition has the following property: the zero function is a pointwise limit, along a subsequence of lengths nk of upper density 1 and with probabilities increasing to 1, of the distribution functions of the normalized (i.e. appropriately scaled) hitting times to cylinder sets of lengths nk. Of course, this is the smallest possible limit distribution. We indicate two classes of systems where at least one more limit distribution coexists, and occurs with the same 'strength' (i.e. for every typical process, along a subsequence of lengths of upper density 1 and with probabilities increasing to 1): in a-mixing systems this is the exponential limit distribution (the largest possible in systems of positive entropy), and in adding machines this is the distribution L(t) = max{0, min{1, t}} (the largest possible distribution for hitting times).