  Abridged. Fast rotating and self-gravitating astrophysical objects suffer
strong deformations from centrifugal forces. If moreover they are magnetized,
they generate an electromagnetic wave that is perturbed accordingly. When
stellar objects are also surrounded by an ideal plasma, a magnetosphere is
formed. We study the electromagnetic configuration of a force-free
magnetosphere encompassing an ideal spheroidal rotating conductor as an inner
boundary. We put special emphasize to millisecond period neutron star
magnetospheres, those showing a significant oblate shape. Force-free solutions
are computed by numerical integration of the time-dependent Maxwell equations
in spheroidal coordinates. Relevant quantities such as the magnetic field
structure, the spin down luminosity, the polar cap rims and the current density
are shown. We find that the force-free magnetic field produced by spheroidal
stars remains very similar to their spherical counterpart. However, the spin
down luminosity slightly decreases with increasing oblateness or prolateness.
Moreover the polar cap area increases and always mostly encompasses the
equivalent spherical star polar cap rims. The polar cap current density is also
drastically affected.
