When one country controls most of another country's affairs, especially international relations, while still allowing it some autonomy, the dominant country is called a suzerain.
In modern world affairs, suzerains are unusual, but history includes a number of them. For example, the Ottoman Empire was the suzerain in its relationships with Moldova, the principality of Serbia, and Wallachia, and for years China was a suzerain to Mongolia. More recently, China has been considered by some to be the suzerain to Tibet, allowing it a small amount of autonomy while controlling it politically.
