  Rapid rotation in massive stars imposes a latitudinal variation in the mass
loss from radiatively driven winds that can lead to enhanced mass loss at the
poles (with little angular momentum loss) and/or equator (with maximal angular
momentum loss). Here we present an examination of the stellar wind lines of the
two O-type stars with the fastest known equatorial velocities, VFTS 102 ($V\sin
i = 610 \pm 30$ km/s; O9:Vnnne+) and VFTS 285 ($V\sin i = 609 \pm 29$ km/s;
O7.5 Vnnn) in the Large Magellanic Cloud. Ultraviolet spectra of both stars
were obtained with the Hubble Space Telescope Cosmic Origins Spectrograph. The
spectrum of VFTS 285 displays a fast outflow in N V and a much slower wind in
Si IV, and we argue that there is a two-wind regime in which mass loss is
strong at the poles (fast and tenuous wind) but dominant at the equator (slow
and dense winds). These ions and wind lines are not present in the spectrum of
the cooler star VFTS 102, but the double-peaked H$\alpha$ emission in its
spectrum implies equatorial mass loss into a circumstellar disk. The results
suggest that in the fastest rotating O-stars, most mass is lost as an
equatorial outflow, promoting angular momentum loss that contributes to a spin
down over time.
