Determining the differential-rotation law of compact stellar objects produced in binary neutron stars mergers or core-collapse supernovae is an old problem in relativistic astrophysics. Addressing this problem is important because it impacts directly on the maximum mass these objects can attain and, hence, on the threshold to black-hole formation under realistic conditions. Using the results from a large number of numerical simulations in full general relativity of binary neutron star mergers described with various equations of state and masses, we study the rotational properties of the resulting hypermassive neutron stars. We find that the angular-velocity distribution shows only a modest dependence on the equation of state, thus exhibiting the traits of "quasiuniversality" found in other aspects of compact stars, both isolated and in binary systems. The distributions are characterized by an almost uniformly rotating core and a "disk." Such a configuration is significantly different from the j -constant differential-rotation law that is commonly adopted in equilibrium models of differentially rotating stars. Furthermore, the rest-mass contained in such a disk can be quite large, ranging from ≃0.03 M☉ in the case of high-mass binaries with stiff equations of state, up to ≃0.2 M☉ for low-mass binaries with soft equations of state. We comment on the astrophysical implications of our findings and on the long-term evolutionary scenarios that can be conjectured on the basis of our simulations.