Synonyms for the phrase "tied on" could include attached, fastened, secured, affixed, joined, connected, tied down, or bound. These words all convey the idea of something being firmly in place or fixed to a certain location. "Attached" implies that something has been added or joined to another object, while "fastened" suggests that something has been secured tightly. "Secured" conveys the idea of something being made safe or protected, while "affixed" emphasizes the act of attaching something to another object. "Joined," "connected," and "tied down" all suggest a sense of being firmly linked or anchored in place.