Jet driving and fragmentation process in collapsing primordial cloud are studied using three-dimensional MHD nested grid simulations. Starting from a rotating magnetized spherical cloud with the number density of n=10^3 cm^-3, we follow the evolution of the cloud up to the stellar density n=10^22 cm^-3. We calculate 36 models parameterizing the initial magnetic and rotational energies (γ_0, β_0). In the collapsing primordial clouds, the cloud evolutions are characterized by the ratio of the initial rotational to magnetic energy, γ_0/β_0. The Lorentz force significantly affects the cloud evolution when γ_0 > β_0, while the centrifugal force is more dominant than the Lorentz force when β_0 > γ_0. When the cloud rotates rapidly with angular velocity of Ω_0 > 10^-17 (n/10^3 cm^-3)^2/3 s^-1 and β_0 > γ_0, fragmentation occurs before the protostar is formed, but no jet appears after the protostar formation. On the other hand, a strong jet appears after the protostar formation without fragmentation when the initial cloud has the magnetic field of B_0 > 10^-9 (n/10^3 cm^-3)^2/3 G and γ_0 > β_0. Our results indicate that proto-Population III stars frequently show fragmentation and protostellar jet. Population III stars are therefore born as binary or multiple stellar systems, and they can drive strong jets, which disturb the interstellar medium significantly, as well as in the present-day star formation, and thus they may induce the formation of next generation stars.

37 pages, 10 figures, Submitted to ApJ, For high resolution figures, see http://astro3.sci.hokudai.ac.jp/~machida/astro-ph.pdf