I also don't discount that there is Turkish blood in most "Turks". However, in all cases, the conquerors were swallowed up by the conquered, just like the Mongols and Manchus in China. The conquerors dictated what language would be spoken, and what customs and traditions could be continued, which had to stop and what religion would be followed. However, they couldn't demographically overwhelm the much larger populations they conquered.

However, their numbers were so limited that a new, hybrid culture arose. The Turks who invaded Anatolia looked like most of my Kazakh friends. That's not the way people in Turkey look today. Of course, try telling them they're mostly Byzantine Greeks who sold out their heritage in exchange for full political and social rights under a nomad culture that had conquered them.