Palais leaf-space manifolds and surfaces carrying holomorphic flows

Given a pair of commuting holomorphic vector fields defined on a neighborhood of $(0,0) \in \mathbb{C}^2$, we discuss the problem of globalizing them as an action of $\mathbb{C}^2$ on a suitable complex surfaces along with some related questions. A review of Palais' theory about globalization of local transformation groups is also included in our discussion.