Median triaxiality of DM halos as function of nonlinear fluctuations of cosmic matter field, σ_NL. All the curves superpose, which means that the cosmological dependence of the mass-triaxiality relations is completely encapsulated in the nonlinear power spectrum. However, when |f_R0| = 10⁻⁶, whatever the neutrino mass, the relation between σ_NL and triaxiality does not identify with the relation obtained for the other models. This occurs specifically from $log({\sigma }_{\mathit{NL}}^{-1})\approx -0.1$, corresponding to a mass of 10¹⁴ h/M_⊙ for the fR6 model, which is, for this model, the characteristic mass where the screening starts. The way the halos collapse and sphericize therefore depends on the gravity model. The screening phenomenon modifies the evolution of the shape of the DM halos, which can no longer be encapsulated in the power spectrum. The divergence in the σ_NL − T relations is then a distinctive marker of the change in the gravity model, which nevertheless remains independent of the neutrino mass.