These are the tiny vessels only slightly wider than a single blood cell that carry blood between the smallest arteries and the smallest veins. Capillaries form a fine network throughout the body's organs and tissues. It's through the thin capillary walls that blood and its constituent cells pass oxygen and nutrients to tissues and receive carbon dioxide and other waste products for excretion. Capillaries are not open to blood flow all the time; they open and close according to each individual organ's requirements for oxygen and nutrients.