  The connection between the long GRBs and Type Ic Supernovae (SNe) has
revealed the interesting diversity: (i) GRB-SNe, (ii) Non-GRB Hypernovae (HNe),
(iii) X-Ray Flash (XRF)-SNe, and (iv) Non-SN GRBs (or dark HNe). We show that
nucleosynthetic properties found in the above diversity are connected to the
variation of the abundance patterns of extremely-metal-poor (EMP) stars, such
as the excess of C, Co, Zn relative to Fe. We explain such a connection in a
unified manner as nucleosynthesis of hyper-aspherical (jet-induced) explosions
Pop III core-collapse SNe. We show that (1) the explosions with large energy
deposition rate, $\dot{E}_{\rm dep}$, are observed as GRB-HNe and their yields
can explain the abundances of normal EMP stars, and (2) the explosions with
small $\dot{E}_{\rm dep}$ are observed as GRBs without bright SNe and can be
responsible for the formation of the C-rich EMP (CEMP) and the hyper metal-poor
(HMP) stars. We thus propose that GRB-HNe and the Non-SN GRBs (dark HNe) belong
to a continuous series of BH-forming stellar deaths with the relativistic jets
of different $\dot{E}_{\rm dep}$.
