On the present shape of the Oort cloud and the flux of “new” comets

•The evolution over 5 Gyr of a sample of 107 Oort cloud comets is performed.•A robust steady state of the Oort cloud is highlighted.•A majority of comets were in the J-S region one orbital period before observability.•For a < 20 000 UA, obs. comets have a preferences for retrograde orbits.•Most of our results are unaffected by the initial energy distribution.