  The phenomenon of s-wave spin triplet Cooper pairs induced in ferromagnetic
metals has been researched now for more than a decade, and its main aspects are
well understood. Crucial in converting s-wave singlet pairs in the
superconductor to s-wave triplets in the ferromagnet is the engineering of
well-defined magnetic inhomogeneity (the 'generator') at the interface with the
superconductor. Vertical layer stacks are typically used as such, where two
separate thin ferromagnetic layers with homogeneous but non-collinear
magnetizations, provide the inhomogeneity. Alternatively, magnetic textures,
like ferromagnetic domain walls and vortices, are possible triplet generators,
although they are far less studied. In this paper we review our experiments on
lateral disk-shaped Josephson junctions where a ferromagnetic bottom layer
provides a weak link with a vortex magnetization imposed by the shape of the
disk. We present three different junction configurations, exhibiting their own
generator mechanism. In the first, we utilize the non-collinearity with a
second ferromagnetic layer to produce the triplet correlations. The second
configuration consists of only the bottom ferromagnet and the superconducting
contacts; it relies on the vortex magnetization itself to generate the
spin-polarized supercurrents. In the third case we exploit an intrinsic
generator by combining a conventional superconductor (NbTi) and a half-metallic
ferromagnetic oxide (La$_{0.7}$Sr$_{0.3}$MnO$_3$). We find strong supercurrents
in all cases. A particularly interesting finding is that the supercurrents are
strongly confined at the rims of the device, independent of the generating
mechanism, but directly related to their triplet nature. What causes these rim
currents remains an open question.
