  Crystal graphs are powerful combinatorial tools for working with the plactic
monoid and symmetric functions. Quasi-crystal graphs are an analogous concept
for the hypoplactic monoid and quasi-symmetric functions. This paper makes a
combinatorial study of these objects. A previously-observed isomorphism of
components of the quasi-crystal graph is explained and explicitly described
using a new combinatorial structure called a quasi-array. Then two conjectures
of Maas-Gari\'epy on the interaction of fundamental quasi-symmetric functions
and Schur functions and on the arrangement of quasi-crystal components within
crystal components are settled, the former positively, the latter negatively.
