  We study Maker--Breaker total domination game played by two players,
Dominator and Staller, on the connected cubic graphs. Staller (playing the role
of Maker) wins if she manages to claim an open neighbourhood of a vertex.
Dominator wins otherwise (i.e.\ if he can claim a total dominating set of a
graph). For certain graphs on $n\geq 6$ vertices, we give the characterization
on those which are Dominator's win and those which are Staller's win.
