  Among about 1.8 million Gaia DR2 high proper motion stars with $\mu>60$
mas/yr and moderately significant parallaxes ($\varpi>3\sigma_{\varpi}$), we
have selected 109 high-speed star candidates with Galactic rest frame
tangential velocities (corrected for solar motion) $v_{t,g}$$>$700 km/s, well
above the local Galactic escape velocity. After applying various Gaia DR2
astrometric quality criteria, only 39 candidates remained, including all three
hypervelocity runaway white dwarfs (HVR WDs) found by Shen et al. (2018) but no
additional such candidates (falling in the same region of the colour-magnitude
diagram). Considering only candidates with highly significant parallaxes
($\varpi>5\sigma_{\varpi}$) as reliable extreme tangential velocity candidates
(cf. Bromley et al. 2018), our final list consists of six objects with
parallaxes of 0.17 mas $\lesssim \varpi \lesssim$ 1.05 mas and tangential
velocities of 730 km/s $\lesssim v_{t,g} \lesssim$ 1600 km/s, including two
candidates of Bromley et al. (2018). Only one of the three HVR WDs of Shen et
al. (2018), D6-2 (= NLTT 51732), falls in that list but can be considered a
doubtful high-speed candidate because of its relatively large astrometric
quality parameters. One of the three new extreme velocity candidates in our
list, Gaia DR2 6097052289696317952, is relatively bright ($G\approx$13.5 mag)
and blue $BP$$-$$RP$$\approx$0.6 mag and has the smallest parallax and highest
tangential velocity. Radial velocity measurements are needed to clarify whether
these high-speed candidates are unbound to the Galaxy.
