Step 1: The CT shows a large vessel entering the liver at the porta hepatis and branching into the right and left intrahepatic divisions. The vessel that classically branches into the liver at the porta is the portal vein.
Step 2: The portal vein (hepatic portal vein) carries blood from the gastrointestinal tract, gallbladder, pancreas and spleen to the liver, delivering nutrients and toxins for processing. It supplies about 75 percent of total hepatic blood flow, the rest coming from the hepatic artery.
Step 3: The distractors are wrong. The SVC drains the upper body into the right atrium, in the thorax. The IVC runs posteriorly and drains into the right atrium; it does not branch into the liver parenchyma. The splenic vein drains the spleen and joins to form the portal vein but does not itself branch into the liver. So the branching structure is the portal vein (option c).