China did have suzerainty over its vassal states (附属国), e.g. Turgesh/Xueyantuo khanate to Tang dynasty(before Tang conquest of the both states), Korea/Vietnam to Ming and Qing dynasties. To understand that, you have to know about some differences between “vassal states” and “tributary states” to China. read more
This list of tributary states of China encompasses suzerain kingdoms from China in Europe, Africa, East Asia, South Asia, Central Asia and Southeast Asia. read more
Thus China was completely surrounded by a chain of smaller tributary states, and this fact helped to establish the belief that the emperor of China was emperor of the whole world. In later times Cochin China, Siam, Burmah either wholly or practically threw off their allegiance, and no longer paid tribute. read more