Phase space of β, the initial ratio of rotational to gravitational energy, vs. core mass M_c. The solid/open circles correspond to models with/without disk fragmentation. In the black region we found formation of sub-stellar- or planetary-mass companions on wide orbits. The dark-shaded region is the region in which both fragmentation and ejection events may occur, and in the light-shaded region occur only fragmentation events. The white area marks the region without fragmentation. Arrows illustrate uncertainties associated with a coarse grid of models and indicate models in the β:   M_c phase space that might have shown (with a 50% probability) disk fragmentation (ejection/companion formation) had we considered a finer grid of models. Each pair of data in parenthesis indicates the mean disk radius and mass for the corresponding model.