The posterior superior alveolar artery (posterior dental artery) is given off from the maxillary, frequently in conjunction with the infraorbital artery

Infraorbital artery

The infraorbital artery is an artery in the head that runs in the maxilla, emerging through the infraorbital foramen, just under the orbit of the eye.-Course:...

 just as the trunk of the vessel is passing into the pterygopalatine fossa

Pterygopalatine fossa

The pterygopalatine fossa is a fossa in the skull. It is the indented area medial to the pterygomaxillary fissure leading into the sphenopalatine foramen.-Boundaries:It has the following boundaries:...

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Branches

Descending upon the tuberosity of the maxilla, it divides into numerous branches, some of which enter the alveolar canals

Alveolar canals

The infratemporal surface of the maxilla is pierced about its center by the apertures of the alveolar canals, which transmit the posterior superior alveolar vessels and nerves....

, to supply the molar

Molar (tooth)

Molars are the rearmost and most complicated kind of tooth in most mammals. In many mammals they grind food; hence the Latin name mola, "millstone"....

 and premolar

Premolar

The premolar teeth or bicuspids are transitional teeth located between the canine and molar teeth. In humans, there are two premolars per quadrant, making eight premolars total in the mouth. They have at least two cusps. Premolars can be considered as a 'transitional tooth' during chewing, or...

 teeth and the lining of the maxillary sinus

Maxillary sinus

The pyramid shaped maxillary sinus is the largest of the paranasal sinuses, and drains into the nose. It is present at birth as rudimentary air cells, and develops throughout childhood.-General characteristics:...

, while others are continued forward on the alveolar process to supply the gingiva

Gingiva

The gingiva , or gums, consists of the mucosal tissue that lies over the mandible and maxilla inside the mouth.-General description:...

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