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Star formation in relic HII regions of the first stars is investigated usingmagneto-hydrodynamical simulations with a nested grid method that covers 10orders of magnitude in spatial scale and 20 orders of magnitude in densitycontrast. Due to larger fraction of H_2 and HD molecules, its prestellarthermal evolution is considerably different from that in the first starformation. Reflecting the difference, two hydrostatic cores appear in a nestedmanner: a protostar is enclosed by a transient hydrostatic core, which appearsduring the prestellar collapse. If the initial natal core rotates fast at arate with rotational to gravitational energy ratio \beta_0 > 0.01-0.1, thetransient hydrostatic core fragments to \sim 10 M_\odot sub-cores at density\sim 10^9 cm^-3. With smaller rotation energy, fragmentation occurs at higherdensity while a single protostar forms without fragmentation if rotation isextremely slow with \beta_0 < 10^-6 -10^-5. If magnetic field is present, thesethreshold values of \beta_0 is boosted owing to angular momentum transport bythe magnetic breaking. Magnetic field also drives the protostellar outflows.With strong magnetic field, two distinct outflows are observed: The slower oneemanates from the transient hydrostatic core, while the faster one from theprotostar. These flows may affect the final stellar mass by ejecting some ofmasses in the initial core, and also may play some role in driving andmaintenance of interstellar turbulence in young galaxies.

Star Formation in Relic HII Regions of the First Stars: Binarity and Outflow Driving