The Mistletoe (宿り木 Yadorigi) is a mysterious familiar in Rewrite.
In the visual novel, its appearance is never shown but is is said to be a forest vine, preserved for hundreds of years.
Being a familiar, it does not have a personality or a mind of its own, but it is specialized in that it has retained and recorded the memories, knowledge, and powers of the summoner that it served long ago. It bestows exceptional summoner powers onto the one capable of using them and in exchange that person has to protect the Key as a Druid.
Kotori's Past: After the events of a car accident that killed her parents, Kotori fled into the woods and found a vine that was the Mistletoe. It offered her the knowledge to restore her parents as familiars in exchange for protecting the Key, though she did not accept the deal right there. Sometime later she finds Kotarou after he had been badly wounded by Kagari, she accepts the deal the Mistletoe in exchange for a way to keep Kotarou alive. Kagari hands Kotori a piece of her ribbons which she infuses with Kotorou's body and from then on becomes a Druid.