Who owns the church's name?
Trademark and brand control — the quietest lever, and the one that does most of the work in newer networks.
The denomination, licensed to the congregation
The denomination — the congregation is a unit of it
No one controls it
Not established
For these bodies the arrangement is not publicly documented. The gap is recorded on each profile with the reason.
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Anglican Church in North America
Built from primary governing documents
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Catholic religious institutes
Partial — some structures are not publicly documented
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Evangelical Lutheran Church in America
Partial — some structures are not publicly documented
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Presbyterian Church (U.S.A.)
Partial — some structures are not publicly documented
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Presbyterian Church in America
Partial — some structures are not publicly documented
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The Episcopal Church
Built from primary governing documents
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The Lutheran Church—Missouri Synod
Built from primary governing documents
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The Order of Friars Minor (Franciscans)
Built from primary governing documents
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The Society of Jesus (Jesuits)
Built from primary governing documents
Every grouping above is a nearest-fit label; the deviations are stated in each profile's prose. Why it is built that way.