Chez Chesler

Over on the Volokh Conspiracy, David Bernstein comments on the BBC apologizing for calling Jerusalem the capital of Israel. This got me wondering, how big is a capital region? For instance, the capital of the US is "Washington, DC" but that city is a lot bigger than the region around the Mall that contains the White House, Capitol, and Supreme Court. Maybe the notion of "city" is so unambiguous that people don't ask the question, since the answer is obviously "the capital region is bounded by the city lines of that city where the seat of government is located". (This is of course setting aside the questions raised in that comment thread of cases where for some reason some or all of the branches of the government actually meet elsewhere, temporarily or permanently, or the base question, of a capital which some other countries ignore, and also the question alluded to by another commenter, the situation where the capital city is not the "Queen" city, such as in New York State, where the most important city is New York, not Albany, or in the USA where the most important city is New York, not Washington.) If the capital of the US were moved back to New York, would we say that the capital is "The City of Greater New York", or would we say "Manhattan" or "Turtle Bay"? What if some of the key buildings, or embassies, were actually in Lake Success, or White Plains, or Murray Hill, NJ?