We study the transverse momentum spectra of identified particles in ultrarelativistic collisions of large and small collision systems. In order to isolate information contained in the momentum dependence, we propose to scale the spectra by the total particle number and mean transverse momentum, global quantities which are already well studied. We observe an interesting, nearly universal, centrality-independent shape in the scaled spectra, similar to scalings that have been studied previously. This scaling behavior breaks down at large transverse momentum and for very small systems, such as those produced in $p-p$ collisions. We perform hybrid hydrodynamic simulations and show that, in these simulations, a centrality-independent shape is a consequence of an event-by-event independence. Our results motivate further theoretical and experimental investigations of the regime of validity of this scaling phenomenon and their physical interpretation at different collision energies and systems.

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