What role did the Donation of Constantine have on the development of the doctrine of Papal supremacy?

In the late Middle Ages, two documents arose which, together, are called the *The Donation of Constantine*. They made a large number of statements which would have had the effect of making the Pope the "Emperor of Christianity." Considering that they were discredited by the end of the 16th century, what effect did these documents have on the development and legitimacy of the Papal claims at primacy?