Mosul and Kirkuk have Kurds, Turks, Arabs. In Mosul, Arabs are more, in Kirkuk they are less. In both, Turks and Kurds are close in numbers.
I personally think Turkey should support independence of Iraqi Kurdistan, if the civil war in Iraq gets out of control. Turkey could even get the Kurds guarantee rights of the 1.5 million Turks living in the north, in exchange for support. I prefer to see the Turks in Mosul and Kirkuk as a minority in a prosperous Kurdistan rather than part of an Iraqi bloodbath (into which civil wars usually turn)
Here is the situation:
1-Kurdish region is landlocked and bordered by Iraq, Iran, Syria, and Turkey.
2-Most of the foreign investment in Northern Iraq comes from Turkey.
3-All of Northern Iraq's oil flows through Turkey.
4-Percent-wise, Iraqi Kurdistan has a larger Turkish minority, than Turkey has a Kurdish minority.
5-Kurds, just like Turks, are one of the few secular muslim peoples.
6-Largest Kurdish population in the world is in Istanbul.
7-Kurds in Turkey are more mixed with Turks than Kurds in Iraq are with Arabs.
8-Kurds in Iraq and Turkey have their differences (I remember the time when Iraqi Kurds asked for help from Turkey against the Kurdish separatist/terrorists from Turkey, after losing 200 peshmerga fighters). They speak different dialects.
9-Here is a map from the latest election in Turkey, shoving the votes recieved by the only party whose main line was improving Kurdish rights, and all candidates Kurds. (Large font provinces have more population)
Keep in mind that not all of this party's voters wanted independence, and not all Kurds voted for this party. Provinces with green and higher in the map have more than half of their populations as Kurdish. So at average half or less of the Kurds in Turkey would even want independence.
10-Since the time of the map above, Turkey introduced many improvments in Kurdish rights, and has to make even more, on the way to EU.
11-Turkey doesn't have many friends in the Middle East.
From these, I deduce
1-Turkey exaggerates fears of its own Kurds getting independent if Iraqi Kurds become so.
2-Turkey is the only neighbor with whom Iraqi Kurds can easily get friendly.
3-It is in Turkey's best interest to turn a Kurdistan into their little brother rather than enemy.
By the way, I am a Turk.
edit: I found out that various statistical institutes and/or researchers (European, American, and Turkish) have calculations of Kurdish population in Turkey varying between 6 and 13% (based on ethnicity, native language, population censi, etc.). I guess the often cited 20% is Kurdish propaganda.