Which condition is characterized by very large amounts of blood in urine?

Hematuria is the medical term that refers specifically to the presence of blood in the urine. It can be classified into two types: gross hematuria, where the blood is visible to the naked eye and gives the urine a reddish appearance, and microscopic hematuria, where blood is only detectable under a microscope. The characteristic of "very large amounts of blood in urine" aligns directly with gross hematuria, making this the correct choice.

The other conditions listed do not correspond to the presence of blood in urine. Epistaxis refers to nosebleeds and is related to bleeding from the nasal cavity. Hemorrhage is a general term for bleeding that can occur internally or externally and is not specific to any body fluid. Hepatomegaly means enlargement of the liver and does not pertain to blood in urine. Thus, hematuria is the most precise term for this condition.