The blood vessel NOT connected to the liver is the:

The inferior vena cava is the blood vessel that is not connected to the liver. Understanding the anatomy and functional relationships of these vessels helps clarify this point.

The hepatic vein carries blood away from the liver, draining deoxygenated blood back into the circulatory system. The hepatic portal vein is crucial as it brings nutrient-rich but deoxygenated blood from the gastrointestinal tract and spleen directly to the liver for processing. The renal vein, on the other hand, drains blood from the kidneys, which although significant in terms of bodily function, does not have a direct connection to the liver.

In contrast, the inferior vena cava is a major vein that carries deoxygenated blood from the lower half of the body back to the heart but does not have a direct connection to liver functions or blood flow. Thus, while the hepatic vein and the hepatic portal vein are specifically linked to liver blood circulation, the renal vein manages blood from the kidneys and the inferior vena cava is involved in systemic circulation without a direct role in hepatic processes. This anatomical relationship highlights why the inferior vena cava is correctly identified as the blood vessel not connected to the liver.