  Within a 400 pc sphere around the Sun, we search for Praesepe's tidal tails
in the Gaia DR2 dataset. We used a modified convergent-point method to search
for stars with space velocities close to the space velocity of the Praesepe
cluster. We find a clear indication for the existence of Praesepe's tidal
tails, both extending up to 165~pc from the centre of the cluster. A total of
1393 stars populate the cluster and its tails, giving a total mass of 794
M_Sun. We determined a tidal radius of 10.77 pc for the cluster and a tidal
mass of 483 M_Sun. The corresponding half-mass radius is 4.8 pc. We also found
clear indication for mass segregation in the cluster. The tidal tails outside 2
tidal radii are populated by 389 stars. The total contamination of our sample
by field stars lies between 50 to 100 stars or 3.6 to 7.2 per cent. We used an
astrometrically and photometrically clean sub-sample of Gaia DR2 which makes
our Praesepe sample incomplete beyond M_G ~ 12.0 mag, which corresponds to
about 0.25 M_Sun. A comparison with an N-body model of the cluster and its
tails shows remarkably good coincidence. Three new white dwarfs are found in
the tails.
