Abstract: 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 $\varepsilon$ whose maximum degree $\Delta(G)$
is sufficiently large. We prove that the list ($d$,1)-total labelling number
$Ch_{d,1}^{\rm T}(G)$ of $G$ is at most $\Delta(G)+2d$.

Key words: (d,1)-total labelling, list (d,1)-total labelling, list (d,1)-total labelling number, graphs