Death Note: Light Vs. L (L's Death Note or shinigami?)

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Since Death Note premeired on Adult Swim, and on 10/27/2007, today's Death Note Ep., "Confrontation", Light (Kira) has accepted L's challenge to find each other. They say that they are both "justice", and the first one to reveal himself will die. This happens as Light killed the wrong "L" to prove the REAL "L"'s point. But in this case, does L also have a Death Note of his own, or even a shinigami like Ryuk, or both?