Hi, 

the Kart Maliks were based mainly in Herat but they were also from other part of modern Afghanistan and yesterdays persian Khorasan. They claimed themself as descends of the Ghurids. When the Il-Khanatas took the power of the whole iranian plateau they accpeted them as their neighbours so they were able to rule self in Khorasan. Just Samarkand and Bukhara and maybe Merv was under the il-Khanatas while the mst of the plateau were under their own hands, even modern Pakistan.

Generally we can say they were a sub-ordinated dynasty..but an indenpendent one unlike other dynasties or nations. I just don´t know who to deal with both because both dynasties were ruling in Greater Iran..