  A tree is scattered if no subdivision of the complete binary tree is a
subtree. Building on results of Halin, Polat and Sabidussi, we identify four
types of subtrees of a scattered tree and a function of the tree into the
integers at least one of which is preserved by every embedding.
  With this result and a result of Tyomkyn, we prove that the tree alternative
property conjecture of Bonato and Tardif holds for scattered trees and a
conjecture of Tyomkin holds for locally finite scattered trees.
