Generally speaking if powers require certain objects or spirits to use them, anyone who would inherit such a power during this Fourth Wall would also gain the necessary object or spirit. Characters can also gain objects that are commonly associated with a power, even if they are not strictly necessary for using it.
For example, in Harry Potter, spell casting is done via wands, so anyone who gets Harry Potter powers will also get a wand. Meanwhile, in The Owl House, many witches have a Palisman wand. This is not a necessary component of their spell casting, but someone who gains these sort of witch powers could also gain a palisman of their own.
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Generally speaking if powers require certain objects or spirits to use them, anyone who would inherit such a power during this Fourth Wall would also gain the necessary object or spirit. Characters can also gain objects that are commonly associated with a power, even if they are not strictly necessary for using it.
For example, in Harry Potter, spell casting is done via wands, so anyone who gets Harry Potter powers will also get a wand. Meanwhile, in The Owl House, many witches have a Palisman wand. This is not a necessary component of their spell casting, but someone who gains these sort of witch powers could also gain a palisman of their own.