Complete algebraic vector fields on affine surfaces-Part II

In this work we finish off the classification of meromorphic semi-complete vector fields announced in Rebelo [J. Geom. Anal 13(4) (2003) 669-696]. As an application of our results, we give a simple and more geometric proof of the classification of complete polynomial vector fields on C2 recently obtained through the works of Brunella and McQuillan.