  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
"quasi-universality" 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 $j-{\rm constant}$ 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 $\simeq
0.03\,M_{\odot}$ in the case of high-mass binaries with stiff equations of
state, up to $\simeq 0.2\,M_{\odot}$ 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.
