I'm a member of the church of where?
Unitarian Universalists will own up to our historic traditions, but get much before 1825 (foundation of the American Unitarian Association) or 1644 (the Cambridge Platform, the North American basis of congregational polity) and the claims get pretty nebulous, even if the legacy is readily apparent.
I'm presently thinking of the geographic parish. This legacy -- that a church's membership, leadership and scope of ministry is tied to a particular area -- comes the Roman or Western church via England. One of our dirtly little secrets -- certainly more on the Unitarian side -- is that many of our oldest congregations are the product of a government interest in established worship, only later to get their walking papers when mature and well-established.
As Unitarians and Universalists moved west, leaving the established civil and religious parishes of New England, they carried the same idea, though often dubbed "societies" but with the same notions of jurisdiction and catchment. We get a strong echo of this in UUA rule 3.3.4, pertaining to multiple congregations in one area, but our custom of naming new congregations after a locale speaks to this. And we still think of our institutions mainly in terms of the legal entities that make particular local decisions, rather than, say, an invisible spiritual bond that trancends space, time or both.
An alternative -- if we're going into history, and they certainly exist, and staying with the visible church -- would be the minster, or monastic church. This would be the centralized ministerial service that would, using our own language, serve satellites by extension. The Church of the Larger Fellowship comes close to this, and its eccentric place in our polity makes it the exception that proves the rule. Christine Robinson and the Albuquerque church's experiment in extension is another example. Indeed, some people make General Assembly or other conferences a major mode of spiritual expression -- shouldn't we recognize this plainly?
I mention it because geography cannot be the strong determiner it once was. We travel faster and farther, and communication technology knits us together better than we once could have had. Even in the nineteeth century, the post and publications functioned as a church for many Universalists, and let congregations ride and fall as the resources permitted. If they could make a go of it then why not now when we have more support for this kind of extended and flexible ministry?