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

Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif