  Current implementations of the stellar atmosphere typically derive boundary
conditions for the interior model from either grey plane-parallel atmospheres
or scaled solar atmospheres, neither of which can be considered to have
appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant
Branch (TP-AGB). This paper discusses the treatment and influence of the outer
boundary condition within stellar evolution codes, and the resulting effects on
the AGB evolution. The complex interaction of processes, such as the third
dredge up and mass loss, governing the TP-AGB can be affected by varying the
treatment of this boundary condition. Presented here are the results from
altering the geometry, opacities and the implementation of a grid of
MARCS/COMARCS model atmospheres in order to improve this treatment. Although
there are changes in the TP-AGB evolution, observable quantities, such as the
final core mass, are not significantly altered as a result of the change of
atmospheric treatment. During the course of the investigation, a previously
unseen phenomena in the AGB models was observed and further investigated. This
is believed to be physical, although arising from specific conditions which
make its presence unlikely. If it were present in stars, this phenomenon would
increase the carbon-star lifetime above 10Myr and increase the final core mass
by $\sim0.1M_{\odot}$ in the narrow initial-mass range where it was observed
($\sim2-2.3M_{\odot}$).
