Which term describes someone who is attempting to show superiority over others?

The term that describes someone attempting to show superiority over others is "pretentious." This word typically refers to individuals who try to impress others by looking or behaving in a way that is exaggerated or intended to create a false impression of their importance or high status. Pretentiousness often involves adopting artificial airs or behaving in a manner that seeks to elevate oneself above peers, demonstrating a desire to be perceived as more significant or knowledgeable than one genuinely is.

The other options do not carry the same connotation of superiority. "Profound" refers to something deep or far-reaching in meaning or significance, but it does not imply superiority over others. "Prodigal" describes someone who is wastefully extravagant, particularly in spending resources, without the notion of superiority. "Profligate" also refers to recklessness, especially regarding spending or behavior, and does not convey a sense of showing superiority over others. Therefore, "pretentious" is the most fitting term for someone attempting to assert dominance or superiority.