Maxillary aery is
Branches of external carotid aery Anterior Superior thyroid Lingual Facial Posterior Occipital Posterior auricular Medial Ascending pharyngeal Terminal Maxillary Superficial temporal Ref BDC volume 3 ;sixth edition pg 101
Branch of facial aery
Branch of internal carotid aery
Branch of common carotid
Terminal branch of external carotid
Head and neck