  [abbreviated] We consider the problem of tidal disruption of a star by a
super-massive Kerr black hole. Using a numerically fast Lagrangian model of the
tidally disrupted star we survey the parameter space of the problem and find
the regions in the parameter space where the total disruption of the star or a
partial mass loss take place as a result of fly-by around the black hole. Our
treatment is based on General Relativity, and we consider the range of the
black hole masses where the tidal disruption competes with the relativistic
effect of direct capture of the star by the black hole. We find that our
results can be 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, referred to as the tidal cross sections, 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. 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 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 $a=0$ the tidal disruption takes place for $M < 5\cdot
10^{7}M_{\odot}$ and when $a\approx 1$ the tidal disruption is possible for $M
< 10^{9}M_{\odot}$.
