Spherical curves that bound immersed discs

Let/be an immersion of the oriented circle in the oriented sphere. Let the image lie in general position and have tangent winding number t with respect to some point oe in its complement. The extensions of/to an orientation preserving immersion of the disc are classified up to topological equivalence by the (0, i(l — i-))-assemblages induced by a star of rays from oo to the complementary components of the curve. Applications to the classification problem of stable maps between closed surfaces are also discussed.