Branchedness is the state of being branched or having branches, and there are several synonyms you can use to refer to this characteristic. One of the most commonly used alternatives is "ramification," which refers to the process of dividing or spreading out into branches or smaller branches. "Branchiness" is another synonym you can use when referring to the state of having branches. "Forking" or "dividing" are additional options that can be used to indicate the act of splitting into two or more branches. Finally, "tree-like" or "arboreal" can be used as adjectives to describe the branched nature of something.