the following we considered only cases with $k$ $\geq$ 3 which we regard as signal. This yields 1543 stars or 2.8% of the BS.

The selection of the parameters $(a,b)$ = (1.2 km s$^{-1}$, 0.5 km s$^{-1}$) in velocity space and ${r_{lim}}$ = 15 pc in positional space turned out to be a reasonable compromise to obtain a significant signal for Praesepe and its tails on one hand and a relatively small noise in the background on the other hand (see Fig.\[Figure1\]). We tentatively kept $a$ and $b$ constant and increased ${r_{lim}}$ up to 25 pc. This resulted in a slight increase of the length of the tails together with a raise of spurious over-densities in the surrounding background created at velocities inconsistent with that of Praesepe. A similar effect occurred when we kept ${r_{lim}}$ constant at 15 pc and increased $(a,b)$ to (1.5 km s$^{-1}$, 0.7 km s$^{-1}$).

We used TOPCAT [@2005ASPC..347...29T] to extract the stars belonging to Praesepe and its tails out of the 1543 stars with $k$ $\geq$ 3. Three manual cuts, first in the $X_P,Y_P$-plane, then in the $\Delta V_{\parallel}$, $\Delta V_{\bot}$-plane and cut in the $X_P,Z_P$-plane were necessary to give the final number (1393) of 