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The pulmonary artery, in purple, running from center to upper right, via Wikipedia
The pulmonary artery leads from the large right ventricle of the heart to the lungs. It's one of the largest blood vessels in the body. It is unique among arteries in that it does not carry oxygenated blood. Instead, it carries de-oxygenated blood back to the lungs to be re-oxygenated and returned to the heart through the pulmonary vein to be distributed to the rest of the body.
A blockage of the artery by a clot, plaque, or fat such that blood is not allowed to flow to the lungs is a pulmonary embolism, a life threatening condition.
The pulmonary artery does not supply the lungs with nutrition. That function is served by the bronchial arteries, which branch off from the aorta.