I've always been wondering this. In books, oftentimes fantasy, things will be capitalized to signify their well... significance. If it is coupled with "the", such as a magical sword called "Sword", would the "the" be capitalized, like "The Sword", or left uncapitalized like "the Sword"? Or, is it stylistically different from writer to writer? This can count with family names too. Like, would we say, "The Corleone Hierarchy", or "the Corleone Hierarchy". Or, "the Corleone hierarchy"?
Unless the article is an inseparable part of the title, it should not be capitalized. Even so, it would ordinarily not be capitalized. So Elvis is the King, even though you always see the article used with it.
If it is actually part of the title then I would capitalise it. The (London) Times is The Times. But the Deputy Prime Minister is the Deputy Prime Minister. The trouble with all of this is that apart from the basic rules everybody is taught in their early school years, "the use of Capitals is largely governed by personal taste" (according to Carey's Mind the Stop).
For the first word of a formal title of a publications, that is certainly true. I will read the third volume of The Lord of the Rings, which is The Return of the King. Note the second the in each case does not get capitalized. But titles of books, periodicals, movies, plays, musical compositions, etc are a different rule than a title applied to a person or object. I will visit the Statue of Liberty, not The Statue of Liberty. Also note that it is proper to italicize a title of a piece of writing, but not the proper name of a person, place, or object; different rules.
If that is the institution, government or body's official name, then both words would be capitalised. If the word 'hierarchy' is used as a description, rather than its name, it shouldn't be capitalised.
And if Corleone refers to the mafia family, I think "the Corleone hierarchy" is used as a description, not a title/name.
