Posterior superior alveolar artery
The posterior superior alveolar artery is a branch of the third (peterygopalatine) part of the maxillary artery.
It branches off within the pterygopalatine fossa and exits via the pterygomaxillary fissure on its way to the maxillary tuberosity. It supplies the upper premolar and molar teeth as well as the maxillary sinus. It accompanies the posterior superior alveolar branches of the maxillary nerve on their way to innervate those same teeth.