In Turkey, the (Kurdish / leftist political party) HDP insists that it seeks only autonomy for a Turkish Kurdistan. Erdogan’s government has imprisoned its leaders, on the grounds that they are informally cooperating with the (Marxist guerrilla group) PKK. (Recall last year’s uprisings and repressions in eastern Turkey.)
In Syria, the (de facto government of Rojava / Syrian Kurdistan) YPG has, with US support, taken most of the IS capitol Raqqa. The other major center of military activity is in connection with the finger of Syrian territory seized by Turkey, in order to prevent the Syrian Kurds from having a contiguous territory. Turkey considers the YPG to be indistinguishable from its own PKK, which it regards as a terrorist group, and fears that an independent Syrian Kurdistan would destabilize Turkey as well.
The Syrian and Iranian governments are mainly concerned to maintain a “Shi’ite crescent” or corridor between non-Kurdish Iraq and regime-controlled Syria. This interest is threatened by the YPG moves against Raqqa.
Iraqi Kurdistan has been de facto independent since the Gulf War. It is territorially divided between two political parties cum militias, the PUK (Patriotic Union of Kurdistan) and KDP (Kurdistan Democratic Party). Barzani (KDP), president of the Kurdish Regional Government, is basically a mafioso, and regional elections have been indefinitely postponed. Another minor, Sulimaniyyah-based party called Gorran (which splintered from the PUK), opposed the referendum.
Iran opposes Kurdish national aspirations for fear that its own Kurds would revolt, and out of support for the Shi’ite-dominated government of Iraq. The big recent news has been that (Iraqi Shi’ite) Popular Mobilization Units have been mobilizing around Kirkuk. These are private militias with Iraqi government backing and Iranian support.
Russia is mainly interested in preserving its basing rights in Syria (which means supporting the Assad regime), and in showing that it is a major geopolitical power. It would be happy to see Syria become a patchwork of autonomous regions, and cares about Iraq only insofar as it impacts its diplomatic relations with Turkey and Iran. The USA mainly wants to see ISIS gone, which means supporting the Kurds as the main group capable of fighting them, all the while trying to manage relations with NATO member Turkey. Turkey would rather see a Muslim Brotherhood type government in Syria, but could live with Assad, and hates the Kurds most of all. The Gulf states are weird–Saudi Arabia hates the Muslim Brotherhood because of the threat Arab democracy would pose to its own regime–but most were rooting for one or another of the Sunni rebel factions, and could live with Assad (an Alawi Shi’ite dictator). These days they also have to focus on relations with one another.
Oil prices are low, which means that Iraqi Kurdistan can’t pay salaries (the US covered them until the referendum), Saudi Arabia is poised to go bankrupt in about a decade, and Baghdad is not looking too good either.
I’m sorry, what was the question again?