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.