  We present a convenient method to generate vector beams of light having
polarization singularities on their axis, via partial spin-to-orbital angular
momentum conversion in a suitably patterned liquid crystal cell. The resulting
polarization patterns exhibit a C-point on the beam axis and an L-line loop
around it, and may have different geometrical structures such as \qo{lemon},
\qo{star}, and \qo{spiral}. Our generation method allows us to control the
radius of L-line loop around the central C-point. Moreover, we investigate the
free-air propagation of these fields across a Rayleigh range.
