What term is best associated with the unification of european states like france and spain under all-powerful monarchs, who used their power to subdue the nobility and bring central order to government?

The answer is absolutism. It is the political policy and exercise of limitless, centralized authority and absolute power, as bestowed especially in a sovereign or dictator. The principle of an absolutist system is that the reigning power is not subject to normalized challenge or check by any other agency, be it judicial, legislative, religious, economic, or electoral. King Louis XIV (1643-1715) of France gave the most acquainted proclamation of absolutism when he said, "L’état, c’est moi" ("I am the state").