Let a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we say that Y precedes X if there exists a surjection f in F of X onto Y. We investigate this relation in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, or open mappings. In particular, we investigate minimal and maximal elements, chains and antichains.