In this talk, we will discuss the multiplicative integer systems on trees, those are countable graphs with no loop, and compute their boundary complexities. In simple terms, the boundary complexity is usually viewed as a local topological entropy of the boundary with width N. First, we first introduce the q-multiplicative subshift on trees (q-MST) and present an explicit formula for the boundary complexity of q-MST whenever the boundary width is finite or infinite. Then, we study the multiple multiplicative subshift on trees. When the subshift is a one-step subshift of finite type, the explicit boundary complexity formula can be obtained. An interesting phenomenon for multiplicative systems is that if the boundary width N tends to infinity, then the boundary complexity of the system is equal to its topological entropy.