  Mass-transfer interactions in binary stars can lead to accretion disk
formation, mass loss from the system and spin-up of the accretor. To determine
the trajectory of the mass-transfer stream, and whether it directly impacts the
accretor, or forms an accretion disk, requires numerical simulations. The
mass-transfer stream is approximately ballistic, and analytic approximations
based on such trajectories are used in many binary population synthesis codes
as well as in detailed stellar evolution codes. We use binary population
synthesis to explore the conditions under which mass transfer takes place. We
then solve the reduced three-body equations to compute the trajectory of a
particle in the stream for systems with varying system mass ratio, donor
synchronicity and initial stream velocity. Our results show that on average
both more mass and more time is spent during mass transfer from a
sub-synchronous donor than from a synchronous donor. Moreover, we find that at
low initial stream velocity the asynchronous rotation of the donor leads to
self-accretion over a large range of mass ratios, especially for
super-synchronous donors. The stream (self-)intersects in a narrow region of
parameter space where it transitions between accreting onto the donor or the
accretor. Increasing the initial stream velocity leads to larger areas of the
parameter space where the stream accretes onto the accretor, but also more
(self-)intersection. The radii of closest approach generally increase, but the
range of specific angular momenta that these trajectories carry at the radius
of closest approach gets broader. Our results are made publicly available.
