So Ryuk stole Shido's death note, and rem 'inherited' Jealous' book. But Ryuk and Rem already had their own so they each have 2. then ryuk and rem each gave a death note to misa and light. once L cornered light and misa, they both gave up ownership of their notes. but not before light buried one of their books, and have rem take the spare one to higuchi. after higuchi was caught the task force got a hold of the death note. then light and misa got their memories back and dug up the spare notebook. then the task note was stolen by mello, but then retrieved. so then light had misa give up hers and sent it to mikami, shido got his back.
So what happened to Rem’s original notebook after she died killing L? I know ryuk still had his orig notebook and killed light at the end.