  We show that conservation of longitudinal magnetization in a spinor
condensate provides a stabilizing mechanism for a coreless vortex
phase-imprinted on a polar condensate. The stable vortex can form a composite
topological defect with distinct small- and large-distance topology: the inner
ferromagnetic coreless vortex continuously deforms toward an outer singular,
singly quantized polar vortex. A similar mechanism can also stabilize a
nonsingular nematic texture in the polar phase. A weak magnetization is shown
to destabilize a coreless vortex in the ferromagnetic phase.
