  Uniaxial nematic liquid crystals whose molecular orientation is subjected to
a tangential anchoring on a curved surface offer a non trivial interplay
between the geometry and the topology of the surface and the orientational
degree of freedom. We consider a general thin film limit of a Landau-de Gennes
Q-tensor model which retains the characteristics of the 3D model. From this,
previously proposed surface models follow as special cases. We compare
fundamental properties, such as alignment of the orientational degrees of
freedom with principle curvature lines, order parameter symmetry and phase
transition type for these models, and suggest experiments to identify proper
model assumptions.
