We consider the problem of tidal disruption of a star by a super-massive rotating black hole .

Using a numerically fast Lagrangian model of a tidally disrupted star developed in our previous works , we survey the parameter space of the problem and find regions where the total disruption of the star or a partial mass loss from the star takes place as a result of fly-by around the black hole .

Our treatment is based on General Relativity , and we consider a range of black hole masses where the tidal disruption competes with the relativistic effect of direct capture of stars by the black hole .
We model the star as a full polytrope with n = 1.5 with the solar mass and radius .
We show that our results can also be used to obtain the amount of mass lost by stars with different stellar masses and radii .

We find that the results can be conveniently represented on the plane of specific orbital angular momenta of the star ( j _ { \theta } ,j _ { \phi } ) .
We calculate the contours of a given mass loss of the star on this plane , for a given black hole mass M , rotational parameter a and inclination of the trajectory of the star with respect to the black hole equatorial plane .
In the following such contours are referred to as the tidal cross sections .

It is shown that the tidal cross sections can be approximated as circles symmetric above the axis j _ { \phi } = 0 , and shifted with respect to the origin of the coordinates in the direction of negative j _ { \theta } .
The radii and shifts of these circles are obtained numerically for the black hole masses in the range 5 \cdot 10 ^ { 5 } M _ { \odot } -10 ^ { 9 } M _ { \odot } and different values of a .
It is shown that when a = 0 tidal disruption takes place for M < 5 \cdot 10 ^ { 7 } M _ { \odot } and when a \approx 1 tidal disruption is possible for M < 10 ^ { 9 } M _ { \odot } .