  The glass transition in binary mixtures of star polymers is studied by mode
coupling theory and extensive molecular dynamics computer simulations. In
particular, we have explored vitrification in the parameter space of size
asymmetry $\delta$ and concentration $\rho_2$ of the small star polymers at
fixed concentration of the large ones. Depending on the choice of parameters,
three different glassy states are identified: a single glass of big polymers at
low $\delta$ and low $\rho_2$, a double glass at high $\delta$ and low
$\rho_2$, and a novel double glass at high $\rho_2$ and high $\delta$ which is
characterized by a strong localization of the small particles. At low $\delta$
and high $\rho_2$ there is a competition between vitrification and phase
separation. Centered in the $(\delta, \rho_2)$-plane, a liquid lake shows up
revealing reentrant glass formation. We compare the behavior of the dynamical
density correlators with the predictions of the theory and find remarkable
agreement between the two.
