  The problem of determining whether a graph $G$ contains another graph $H$ as
a minor, referred to as the minor containment problem, is a fundamental problem
in the field of graph algorithms. While it is NP-complete when $G$ and $H$ are
general graphs, it is sometimes tractable on more restricted graph classes.
This study focuses on the case where both $G$ and $H$ are trees, known as the
tree minor containment problem. Even in this case, the problem is known to be
NP-complete. In contrast, polynomial-time algorithms are known for the case
when both trees are caterpillars or when the maximum degree of $H$ is a
constant. Our research aims to clarify the boundary of tractability and
intractability for the tree minor containment problem. Specifically, we provide
dichotomies for the computational complexities of the problem based on three
structural parameters: the diameter, pathwidth, and path eccentricity.
