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.