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The New Pope

If the person elected is not already a bishop, he shall immediately be ordained bishop. The successful candidate is then asked by the Dean of the College of Cardinals, "Do you accept your canonical election as Supreme Pontiff?" When he gives his agreement (which he can refuse) he is then asked what name he will choose as Pope. This agreement and choice is then signed and (assuming that the person is already a bishop) he immediately becomes Bishop of Rome. The cardinals pay him their respects and the Cardinal Deacon announces the result of the election to the people in St. Peter's Square:

Nuntio Vobis Gaudium Magnum
I announce a Great Joy to You All
Habemus Papam...
We have a Pope....

The new Pope comes out and gives them his blessing. There is no longer a coronation ceremony, but the pontificate is inaugurated at a ceremony in St Peter's a short time afterwards - in the case of Pope John Paul II it was six days later.