  We theoretically examine generation of spin-polarized current using
multi-terminated quantum dot with spin-orbit interaction. First, a two-level
quantum dot is analyzed as a minimal model, which is connected to $N$ ($\ge 2$)
external leads via tunnel barriers. When an unpolarized current is injected to
the quantum dot from a lead, a polarized current is ejected to others,
similarly to the spin Hall effect. In the absence of magnetic field, the
generation of spin-polarized current requires $N \ge 3$. The polarization is
markedly enhanced by resonant tunneling when the level spacing in the quantum
dot is smaller than the level broadening due to the tunnel coupling to the
leads. In a weak magnetic field, the orbital magnetization creates a
spin-polarized current even in the two-terminal geometry (N=2). The numerical
study for generalized situations confirms our analytical result using the
two-level model.
