Always capitalized, including common nouns or adjectives which are essential parts. A common noun used alone as a substitute for the proper noun is not capitalized unless it is a very well-known form, e.g. 'the Capitol' (Washington, DC), 'the Channel' (English Channel). The plural of a common noun which is an essential part of a proper noun is also capitalized, as '10th and I Streets'. The article 'the' is capitalized if it is part of a formal title, address, document title or part, or other proper noun. When the proper noun is used as an adjective, e.g. 'the New York area', or is used to refer to a proper noun, e.g. 'the Queen Mary', 'the' is not capitalized.
Words/phrases which are derivatives of a proper noun are capitalized when their meaning is directly referring to the proper noun, e.g. 'Victorian house', 'Roman architecture'. If the word/phrase has taken on its own meaning or a specialized meaning, it is not capitalized, e.g. 'frankfurter', 'graham cracker', 'india ink', 'manila envelope'.
Military, nobility, organizational, religious, and other formal titles (i.e. formal title) are capitalized before a person's name. But when used in apposition, e.g. 'the archbishop of Canterbury', 'the emperor Ling-Lang', the title is lowercased. In formal usage, as an acknowledgment or introduction, a title following a name and set off by commas is capitalized, e.g. 'I wish to thank R.R.K. Hartmann, Professor of Linguistics, University of Exeter'. Titles used in direct address are also capitalized, e.g. 'Your table is ready, Professor'.