  We study the solution space of general relativistic, axisymmetric, equilibria
of differentially rotating neutron stars with realistic, nuclear equations of
state. We find that different types of stars, which were identified by earlier
works for polytropic equations of state, arise for realistic equations of
state, too. Scanning the solution space for the sample of realistic equations
of state we treat, we find lower limits on the maximum rest masses supported by
cold, differentially rotating stars for each type of stars. We often discover
equilibrium configurations that can support more than 2 times the mass of a
static star. We call these equilibria "\"ubermassive", and in our survey we
find \"ubermassive stars that can support up to 2.5 times the maximum rest mass
that can be supported by a cold, non-rotating star with the same equation of
state. This is nearly two times larger than what previous studies employing
realistic equations of state had found, and which did not uncover \"ubermassive
neutron stars. Moreover, we find that the increase in the maximum rest mass
with respect to the non-spinning stellar counterpart is larger for moderately
stiff equations of state. These results may have implications for the lifetime
and the gravitational wave and electromagnetic counterparts of hypermassive
neutron stars formed following binary neutron star mergers.
