Distributions of the largest fragment charge, Zmax, in multifragmentation reactions around the Fermi energy can be decomposed into a sum of a Gaussian and a Gumbel distribution, whereas at much higher or lower energies one or the other distribution is asymptotically dominant. We demonstrate the same generic behavior for the largest cluster size in critical aggregation models for small systems, in or out of equilibrium, around the critical point. By analogy with the timedependent irreversible aggregation model, we infer that Zmax distributions are characteristic of the multifragmentation time-scale, which is largely determined by the onset of radial expansion in this energy range. Introduction In central heavy-ion collisions at beam energies of ∼20-150 MeV/A multiple production of nuclear fragments can be observed, compatible with the quasi-simultaneous break-up of finite pieces of excited nuclear matter [1][2][3][4][5][6][7]. This so-called "nuclear multifragmentation" is a fascinating process [8] which has long been associated with a predicted liquid-gas coexistence region in the nuclear matter phase diagram at sub-critical temperatures and sub-saturation densities [9][10][11]. Statistical [12][13][14][15][16][17][18][19] and dynamical [20][21][22][23][24] aspects have been widely studied, and evidences supporting equally well either a continuous phase transition of the liquid-gas universality class [13,14,[25][26][27][28][29][30], a discontinuous ("first-order") transition occurring within the coexistence region [29][30][31][32][33][34][35], or indeed the survival of initial-state correlations in a purely dynamical picture [36,37] have been presented. This state of affairs well demonstrates the difficulty of quantitatively identifying a phase transition in small systems such as atomic nuclei, where finite-size effects blur the nature of the transition [38][39][40] whose order may indeed change with the size of the system [29,30], along with the importance of long-range Coulomb forces [4,19,41,42], and presence of dynamical effects such as radial flow [43][44][45][46][47][48][49].In this context we have tried to establish generic features of multifragmentation in order to deduce its nature in a less model-dependent way. In our previous works [50], we used the model-independent universal fluctua-