  A considerable effort has been dedicated recently to the construction of
generic equations of state (EOSs) for matter in neutron stars. The advantage of
these approaches is that they can provide model-independent information on the
interior structure and global properties of neutron stars. Making use of more
than $10^6$ generic EOSs, we asses the validity of quasi-universal relations of
neutron star properties for a broad range of rotation rates, from slow-rotation
up to the mass-shedding limit. In this way, we are able to determine with
unprecedented accuracy the quasi-universal maximum-mass ratio between rotating
and nonrotating stars and reveal the existence of a new relation for the
surface oblateness, i.e., the ratio between the polar and equatorial proper
radii. We discuss the impact that our findings have on the imminent detection
of new binary neutron-star mergers and how they can be used to set new and more
stringent limits on the maximum mass of nonrotating neutron stars, as well as
to improve the modelling of the X-ray emission from the surface of rotating
stars.
