  Solitary stars that wander too close to their galactic centres can become
tidally disrupted, if the tidal forces due to the supermassive black hole
(SMBH) residing there overcome the self-gravity of the star. If the star is
only partially disrupted, so that a fraction survives as a self-bound object,
this remaining core will experience a net gain in specific orbital energy,
which translates into a velocity "kick" of up to $\sim 10^3$ km/s. In this
paper, we present the result of smoothed particle hydrodynamics (SPH)
simulations of such partial disruptions, and analyse the velocity kick imparted
on the surviving core. We compare $\gamma$ = 5/3 and $\gamma$ = 4/3 polytropes
disrupted in both a Newtonian potential, and a generalized potential that
reproduces most relativistic effects around a Schwarzschild black hole either
exactly or to excellent precision. For the Newtonian case, we confirm the
results of previous studies that the kick velocity of the surviving core is
virtually independent of the ratio of the black hole to stellar mass, and is a
function of the impact parameter $\beta$ alone, reaching at most the escape
velocity of the original star. For a given $\beta$, relativistic effects become
increasingly important for larger black hole masses. In particular, we find
that the kick velocity increases with the black hole mass, making larger kicks
more common than in the Newtonian case, as low-$\beta$ encounters are
statistically more likely than high-$\beta$ encounters. The analysis of the
tidal tensor for the generalized potential shows that our results are robust
lower limits on the true relativistic kick velocities, and are generally in
very good agreement with the exact results.
