The state, condition, or quality of being a demon; demonic existence or nature.
From demon + -ship (a suffix creating nouns meaning 'the state or rank of'). The -ship suffix appears in friendship, membership, and kingship, making demonship the parallel construction for demonic status.
The -ship suffix is wild—it transforms any noun into an abstract state: friendship, leadership, craftsmanship—so technically 'demonship' should mean 'the state of being a demon,' but the word is so rare it's basically invisible in modern English.
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