The office, position, or tenure of a conrector; the status or authority held by a joint rector.
From 'conrector' plus the suffix '-ship' (denoting office or status), following the pattern of 'rectorship,' 'professorship,' etc.; indicates shared administrative authority.
The word 'conrectorship' is charmingly bureaucratic—it's the kind of formal title that would appear in old university charters and faculty disputes, describing a system where two people had to agree to run an institution!
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