  We report results from a systematic study of the competition of exotic
triplet pair density wave (PDW) superconductivity (SC) with homogeneous (zero
pair momentum) SC in strongly polarized media such as half metallic systems.
From the two different PDW states allowed by symmetry in this background only
one may dominate or even coexist with homogeneous SC. We propose a direct
experimental identification of PDW SC in this context. Our results suggest that
these exotic states may plausibly emerge in heterostructures involving
proximity of SC with half-metallic CrO$_2$ where induced SC is established in
the half metallic region and in strongly ferromagnetic superconductors.
