Haemoglobin [edit]. The main role of the transport system is to transport oxygen from the alveoli to where it is needed-cells around the body, and this is achieved in the protein haemoglobin.Each haemoglobin molecule can hold four oxygen molecules.he function of the arteries is to transport blood swiftly and at high blood pressure to the tissues. Look at the diagram on the right. It is of a artery and shows three things-the tunica intima, the tunica media and the tunica externa.