Making the world better, one answer at a time. Veins hold the greatest volume of blood: Veins= about 1/2 Heart and lungs= about 1/4 Arteries= about 1/4 Capillaries= about 5%. Veins hold the greatest volume of blood: Veins= about 1/2 Heart and lungs= about 1/4 Arteries= about 1/4 Capillaries= about 5%. Minor edit?