  The game total domination number, ${\gamma_{g}^{t}}$, was introduced by
Henning et al.\ in 2015. In this paper we study the effect of vertex
predomination on the game total domination number. We prove that
${\gamma_{g}^{t}}(G|v) \geq {\gamma_{g}^{t}}(G) - 2$ holds for all vertices $v$
of a graph $G$ and present infinite families attaining the equality. To achieve
this, some new variations of the total domination game are introduced. The
effect of vertex removal is also studied. We show that ${\gamma_{g}^{t}}(G)
\leq {\gamma_{g}^{t}}(G-v) + 4$ and ${\gamma_{g}^{t}}'(G) \leq
{\gamma_{g}^{t}}'(G-v) + 4$.
