  We study asymptotics of Tesler matrices using Kostant pictures, as well as
partial orders on these. We show that the Lusztig data partial order on Kostant
pictures refines the 'merge' partial order on Kostant pictures, and that the
merge partial order on Kostant pictures is equivalent to a partial order on
Tesler matrices. This equivalence requires integral flow graphs. Using Kostant
pictures we find logarithmic asymptotics of some families of Tesler matrices.
