  In this paper we present a complete characterization of the smallest sets
that block all the simple spanning trees (SSTs) in a complete geometric graph.
We also show that if a subgraph is a blocker for all SSTs of diameter at most
4, then it must block all simple spanning subgraphs, and in particular, all
SSTs. For convex geometric graphs, we obtain an even stronger result: being a
blocker for all SSTs of diameter at most 3 is already sufficient for blocking
all simple spanning subgraphs.
