ABSTRACT. In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the 3-dimensional Euclidean space or in the 3-dimensional sphere is parabolic. In the case of ends of revolution in the hyperbolic 3-dimensional space, we find sufficient conditions to attain parabolicity for complete ends of revolution using their relative position to the complete flat surfaces of revolution. This paper is concerned with the study of the conformal type (parabolicity or nonparabolicity) of complete ends of revolution immersed in the 3-dimensional Euclidean space R 3 , in the 3-dimensional hyperbolic space H 3 , or in the 3-dimensional sphere S 3 . Let us denote by M 3 (κ) the simply connected space form of constant sectional curvature κ ∈ R. Hence,is a complete end of revolution if there exists a geodesic in M 3 (κ) such that the end is invariant by the group of rotations of M 3 (κ) that leaves this geodesic point-wise fixed. More precisely, an end of revolution will be the rotation along a geodesic ray γ of M 3 (κ) of a generating smooth curve β : [0, ∞) → M 2 (κ) contained in a totally geodesic 2010 Mathematics Subject Classification. Primary 53C20 53C40; Secondary 53C42.