Context :

Aims : Within a 400 pc sphere around the Sun , we search for Praesepe ’ s tidal tails in the Gaia DR2 dataset .

Methods : We used a modified convergent-point method to find stars with space velocities close to the space velocity of the Praesepe cluster .

Results : 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 _ { \odot } .
We determined a tidal radius of 10.77 pc for the cluster and a tidal mass of 483 M _ { \odot } .
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 \% .
We used an astrometrically and photometrically clean sub-sample of Gaia DR2 which makes our Praesepe sample incomplete beyond M _ { G } \approx 12.0 mag , which corresponds to about 0.25 M _ { \odot } .
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 .

Conclusions :