  This is the first in a series of four papers (with research announcement
posted on this arXiv) that together develop a decomposition theory for
subgroups of Out(F_n).
  In this paper we develop further the theory of geometric EG strata of
relative train track maps originally introduced in the work of Bestvina,
Feighn, and Handel on the Tits alternative, with our focus trained on certain
2-dimensional models of such strata called "geometric models" and on the
interesting properties of these models. A secondary purpose of this paper is to
serve as a central reference for the whole series regarding basic facts of the
general theory for elements of Out(F_n).
