In Death Note, Teru Mikami starts to kill criminals as well as light, but where did his death note come from if there was no shingami attached to it ?
The Death Note was given to Teru Mikami by Amane Misa on Light Yagami's orders. Misa gave up her ownership of that Death Note and lost all memory of it. That Death Note's death god/shinigami is Ryuk, as is the one in possession by the police, however that Death Note is owned by Light Yagami. One of these Death Notes were originally Rem's own Death Note, but was obtained by Light after her death. I assume that Light somehow made Ryuk the shinigami of both death notes, as Light's father obtained the shinigami eyes from the one that is not in possession of Mikami. Therefore Ryuk might be able to follow any of the two owners of the two death notes.