What is the form of blood fat that carries cholesterol out from the liver to other parts of the body?

The correct answer is lipoprotein.

Since cholesterol is insoluble in water, it needs to be packed for transport through the blood. Very low-density lipoproteins (VLDL)  and high-density lipoproteins (HDL) are small particles which contain triacylglycerols, cholesterol, cholesterol esters and the apoproteins. The function of those particles is to transport fats from the liver and distribute them throughout the body. Low-density lipoprotein (LDL) is one of the main groups of lipoprotein which also transport fat molecules (exept triacylglycerols)  around the body.