  Young massive stars in the halo are assumed to be runaway stars from the
Galactic disk. Possible ejection scenarios are binary supernova ejections (BSE)
or dynamical ejections from star clusters (DE). Hypervelocity stars (HVSs) are
extreme runaway stars that are potentially unbound from the Galaxy. Powerful
acceleration mechanisms such as the tidal disruption of a binary system by a
supermassive black hole (SMBH) are required to produce them. Therefore, HVSs
are believed to originate in the Galactic center (GC), the only place known to
host an SMBH. The second Gaia data release (DR2) offers the opportunity of
studying HVSs in an unprecedented manner. We revisit some of the most
interesting high-velocity stars, that is, 15 stars for which proper motions
with the Hubble Space Telescope were obtained in the pre-Gaia era, to unravel
their origin. By carrying out kinematic analyses based on revised
spectrophotometric distances and proper motions from Gaia DR2, kinematic
properties were obtained that help constrain the spatial origins of these
stars. Stars that were previously considered (un)bound remain (un)bound in
Galactic potentials favored by Gaia DR2 astrometry. For nine stars (five
candidate HVSs plus all four radial velocity outliers), the GC can be ruled out
as spatial origin at least at $2\sigma$ confidence level, suggesting that a
large portion of the known HVSs are disk runaway stars launched close to or
beyond Galactic escape velocities. The fastest star in the sample, HVS3, is
confirmed to originate in the Large Magellanic Cloud. Because the ejection
velocities of five of our non-GC stars are close to or above the upper limits
predicted for BSE and DE, another powerful dynamical ejection mechanism (e.g.,
involving massive perturbers such as intermediate-mass black holes) is likely
to operate in addition to the three classical scenarios mentioned above.
