  Many giant exoplanets are found near their Roche limit and in mildly
eccentric orbits. In this study we examine the fate of such planets through
Roche-lobe overflow as a function of the physical properties of the binary
components, including the eccentricity and the asynchronicity of the rotating
planet. We use a direct three-body integrator to compute the trajectories of
the lost mass in the ballistic limit and investigate the possible outcomes. We
find three different outcomes for the mass transferred through the Lagrangian
point $L_{1}$: (i) self-accretion by the planet, (ii) direct impact on the
stellar surface, (iii) disk formation around the star. We explore the parameter
space of the three different regimes and find that at low eccentricities,
$e\lesssim 0.2$, mass overflow leads to disk formation for most systems, while
for higher eccentricities or retrograde orbits self-accretion is the only
possible outcome. We conclude that the assumption often made in previous work
that when a planet overflows its Roche lobe it is quickly disrupted and
accreted by the star is not always valid.
