Are there any CS-trees named after flora-trees?
Robert Tarjan defines the palm tree in "Depth-first search and linear graph algorithms" (1972):


  Let $P$ be a directed graph of two disjoint edge sets, denoted 
  $v \rightarrow w$ and $v \overset{-}{\rightarrow} w$ respectively. If $P$
  satisfies the following properties:
  
  
  The subgraph $T$ containing the edges $v \rightarrow w$ is a
   spanning tree of $P$;
  Each edge not in $T$ connects a vertex with one of its ancestors in
   $T$.  The edges $v \overset{-}{\rightarrow} w$ are called the fronds of $P$.
  


e.g., 



He goes on to prove that the directed graph generated by a depth-first search of a connected graph is a palm tree.

In Collective Tree Spanners and Routing in AT-free Related Graphs, Dragan, Yan, and Corneil  construct a specific spanning tree that they call a willow-tree.