Every planar graph with $\mathrm{\Delta }⩾8$ is totally $(\mathrm{\Delta }+2)$-choosable

Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally $k$-choosable if for any list assignment of $k$ colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree $\mathrm{\Delta }$ needs at least $\mathrm{\Delta }+1$ colors. In the planar case, Borodin proved in 1989 that $\mathrm{\Delta }+2$ colors suffice when $\mathrm{\Delta }$ is at least 9. We show that this bound also holds when $\mathrm{\Delta }$ is $8$.