Prior to World War 1 the Kurds were subjects of the Ottoman empire, and while ethnic minorities, they were (and still are today) majority Sunni Muslim. Under the Millet system they were afforded greater opportunities than other ethnic miorities like the Armenians who were generally christian. The size of Kurdistan is somewhat of a moot point because under Ottoman administration there was no entity known as Kurdistan in and of its self. People identified more closely with their tribe, town, and land more so than with ideas of a greater nationalist calling. Those principals arose more poignantly after the conclusion of World War 1 and the demarcation of interests through Sykes-Picot, Sevres, and Lausanne.

Kurds enjoyed some forms of autonomy under Ottoman rule such as the ability to conduct their affairs in Kurdish and other powers over local governance and affairs. This would change dramatically towards the conclusion of World War I towards the situation more reminiscent of today's realm of kurdish nationalism. The size of Kurdistan prior to World War I reflected really the ethnic distribution of Kurds and the ability with which they were able to exact autonomy from the central Ottoman authorities. Kurdistan as an entity or state is difficult to assess in this context

Kurds are native to Middle east and that doesn't include what is now Turkey. The so called turkish kurdistan was Armenia till 1915.

Armenia was ruled by muslims for quite some time (arabs, mongols, turks) so they considered muslim kurds to be more "reliable" so encouraged them to move to the predominantly christian populated regions and eventually replace them. Actually, Armenians were forced to pay taxes to kurds during the Ottoman times and this led to a lot of tensions. In some cases Armenians were even considered property of kurdish aghas.

Ottomans have used kurds during the genocide too(in "kill the unbelievers" style). And after the Genocide they were allowed to take all the Armenian homes and property.