  The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this
paper, we consider the list version of (d,1)-total labelling of graphs. Let G
be a graph embedded in a surface with Euler characteristic $\epsilon$ whose
maximum degree $\Delta(G)$ is sufficiently large. We prove that the (d,1)-total
choosability $C_{d,1}^T(G)$ of $G$ is at most $\Delta(G)+2d$.
