aÂ·nasÂ·toÂ·moÂ·sis. (É-nÄsâ²tÉ-mÅâ²sÄ­s) n. pl. aÂ·nasÂ·toÂ·moÂ·ses (-sÄz) 1. The connection of separate parts of a branching system to form a network, as of leaf veins, blood vessels, or a river and its branches.