A variety of supersymmetric models give rise to a split mass spectrum characterized by very heavy scalars but sub-TeV gauginos, usually with a wino-like LSP. Such models predict a thermally-produced underabundance of wino-like WIMP dark matter so that non-thermal DM production mechanisms are necessary. We examine the case where theories with a wino-like LSP are augmented by a Peccei-Quinn sector including an axion-axino-saxion supermultiplet in either the SUSY KSVZ or SUSY DFSZ models and with/without saxion decays to axions/axinos. We show allowed ranges of PQ breaking scale f_a for various cases which are generated by solving the necessary coupled Boltzmann equations. We also present results for a model with radiatively-driven naturalness but with a wino-like LSP.

25 pages including 14 .png figures