  Motivated by the study of the structure of algebraic actions the additive
group on affine threefolds X, we consider a special class of such varieties
whose algebraic quotient morphisms X $\rightarrow$ X//Ga restrict to principal
homogeneous bundles over the complement of a smooth point of the quotient. We
establish basic general properties of these varieties and construct families of
examples illustrating their rich geometry. In particular, we give a complete
classification of a natural subclass consisting of threefolds X endowed with
proper Ga-actions, whose algebraic quotient morphisms $\pi$ : X $\rightarrow$
X//Ga are surjective with only isolated degenerate fibers, all isomorphic to
the affine plane A 2 when equipped with their reduced structures.
