When I say "What Kurds want" I mean Kurds in general, but specifically I am talking about the Kurds in Iraqi (south) Kurdistan.
The hottest issue is the reunification of the Kurdish administrations. Currently there are two Kurdistan governments (strange huh ?!)...The PUK controls Sulaimani and some parts of Erbil (Hawler) governate, the KDP controls Erbil and Duhok governates. Both Kurdish parties have influence in Kirkuk but Kirkuk is still under the control of the (New) Iraqi government.
Since 1994, the united Kurdistan Regional Government split up between KDP and PUK. In 1998, when both parties decided to end the civil war, they decided to reunify their governments (but today is 2004 and nothing has happened).
People are very angry at the Kurdish parties. Kurds now think "Why we blame the west and Iran/Turkey/Iraq/Syria for dividing Greater Kurdistan while PUK/KDP have divided South Kurdistan into 2 pieces ?
What Kurds want now is the reunification of the Kurdish administrations, a fair general elections in Kurdistan, and actually practicing democracy as well as stopping the massive corruption in the both Kurdish administrations.
Next : The reality of the Kurdish democracy