Final answer:
The hepatic veins are likely responsible for the production of Ascitic fluid, as they are involved in drainage of the liver and can contribute to portal hypertension and ascites in the event of liver disease.
Step-by-step explanation:
The veins likely responsible for the production of Ascitic fluid are the hepatic veins. Ascites, the accumulation of fluid in the peritoneal cavity, often occurs in the context of liver disease such as cirrhosis, which leads to hypertension in the portal vein. The increased pressure in the portal vein system, a result of the resistance to blood flow through the damaged liver, can cause fluid to leak from the surface of the liver and intestine into the abdominal cavity. Since hepatic veins drain blood from the liver into the inferior vena cava, any blockage or damage to these veins can contribute to increased portal hypertension and consequently to the development of ascites.