  The notion of first order convergence of graphs unifies the notions of
convergence for sparse and dense graphs. Ne\v{s}et\v{r}il and Ossona de Mendez
[J. Symbolic Logic 84 (2019), 452-472] proved that every first order convergent
sequence of graphs from a nowhere-dense class of graphs has a modeling limit
and conjectured the existence of such modeling limits with an additional
property, the strong finitary mass transport principle. The existence of
modeling limits satisfying the strong finitary mass transport principle was
proved for first order convergent sequences of trees by Ne\v{s}et\v{r}il and
Ossona de Mendez [Electron. J. Combin. 23 (2016), P2.52] and for first order
sequences of graphs with bounded path-width by Gajarsk\'y et al. [Random
Structures Algorithms 50 (2017), 612-635]. We establish the existence of
modeling limits satisfying the strong finitary mass transport principle for
first order convergent sequences of graphs with bounded tree-width.
