  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.
