  Let X be a normal affine T-variety, where T stands for the algebraic torus.
We classify Ga-actions on X arising from homogeneous locally nilpotent
derivations of fiber type. We deduce that any variety with trivial
Makar-Limanov (ML) invariant is birationally decomposable as Y\times P^2, for
some Y. Conversely, given a variety Y, there exists an affine variety X with
trivial ML invariant birational to Y\times P^2. Finally, we introduce a new
version of the ML invariant, called the FML invariant. According to our
conjecture, the triviality of the FML invariant implies rationality. This
conjecture holds in dimension at most 3.
