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We present a detailed analysis of dark matter halo shapes, studying how thedistributions of ellipticity, prolateness and axial ratios evolve as a functionof time and mass. With this purpose in mind, we analysed the results of threecosmological simulations, running an ellipsoidal halo finder to measuretriaxial halo shapes. The simulations have different scales, mass limits andcosmological parameters, which allows us to ensure a good resolution andstatistics in a wide mass range, and to investigate the dependence of haloproperties on the cosmological model. We confirm the tendency of haloes to beprolate at all times, even if they become more triaxial going to higherredshifts. Regarding the dependence on mass, more massive haloes are also lessspherical at all redshifts, since they are the most recent forming systems andso still retain memory of their original shape at the moment of collapse. Wethen propose a rescaling of the shape-mass relations, using the variable $\nu =\delta_{c}/\sigma$ to represent the mass, which absorbs the dependence on bothcosmology and time, allowing to find universal relations between halo massesand shape parameters (ellipticity, prolateness and the axial ratios) which holdat any redshift. This may be very useful to determine prior distributions ofhalo shapes for observational studies.

Some like it triaxial: the universality of dark matter halo shapes and their evolution along the cosmic time