Final answer:
The hepatic portal vein supplies the digestive tract and major abdominal organs with partially deoxygenated blood containing nutrients absorbed from the small intestine to the liver for processing.
Step-by-step explanation:
The hepatic vessel that supplies the digestive tract and major abdominal organs is the Hepatic Portal Vein. The hepatic portal vein carries partially deoxygenated blood containing nutrients absorbed from the small intestine to the liver for processing before it is sent to the systemic circulation. This vein actually supplies more oxygen to the liver compared to the hepatic artery.