The descending palatine artery branches off of the maxillary artery in the pterygopalatine fossa and descends through the greater palatine canal along with the greater palatine nerve (from the pterygopalatine ganglion).
In the region of the pterygopalatine fossa, the descending palatine artery separates from the maxillary artery and travels down the greater palatine canal alongside the greater palatine nerve that originates from the pterygopalatine ganglion.