The antonym for the phrase "are an adjunct of" would be "are independent of" or "are not connected to". The term "adjunct" refers to something that is added or attached to something else, indicating that the subject in question is dependent on the main entity. Therefore, the antonyms imply a sense of self-reliance and detachment from the primary structure. In real-world scenarios, such lexical opposites are often used to convey a sense of autonomy, freedom, and a lack of subservience. For example, a business that operates independently of a larger parent organization could be described as not being an adjunct of that company.