“The keys of the kingdom of God—the right and power of eternal presidency by which the earthly kingdom is governed—these keys, having first been revealed from heaven, are given by the spirit of revelation to each man who is both ordained an Apostle and set apart as a member of the Council of the Twelve.

“But since keys are the right of presidency, they can only be exercised in their fulness by one man on earth at a time. He is always the senior Apostle, the presiding Apostle, the presiding high priest, the presiding elder. He alone can give direction to all others, direction from which none is exempt.

“Thus, the keys, though vested in all of the Twelve, are used by any one of them to a limited degree only, unless and until one of them attains that seniority which makes him the Lord’s anointed on earth.

“It follows that when Joseph Smith—sent to a martyr’s death by evil and murderous men—gasps his last breath, Brigham Young, being the next senior officer in the earthly kingdom, automatically becomes its presiding officer.

“The next breath drawn by Brother Brigham is the breath of power filling the lungs of the Lord’s previously anointed servant. There is not so long a time as the twinkling of an eye when the Church is without a presiding officer.”

– Bruce R. McConkie, “The Keys of the Kingdom,” General Conference April 1983.

“It is significant to note just what took place at the time of the passing of President Harold B. Lee. President Romney had been called to the hospital and as they talked, President Lee, realizing that he might be incapacitated for some time, said to President Romney: ‘President Tanner is away, and I want you to take over and carry on the affairs of the Church.’ President Kimball, who came in later, offered his services to President Romney. However, immediately upon the announcement of President Lee’s passing, President Romney turned to President Kimball and said: ‘You, as the president of the Quorum of the Twelve, are now in charge. I am at your disposal and prepared to do anything I can to help.’

“This was entirely in keeping with the order of the Church and is a great example of how the Church is never left without a presidency and how smoothly it passes from one to another. Immediately President Kimball, as president of the Twelve, became the presiding authority of the Church.”

* * *

“President Kimball, the president of the Twelve, called the members of the Twelve together in the upper room of the temple for the purpose of discussing the reorganization of the First Presidency and to take whatever action was decided upon. Those who had been counselors to the President—that is, President Romney and myself—took their respective places in the Quorum of the Twelve.

“President Kimball, upon expressing his great sorrow at the passing of President Lee and his feeling of inadequacy, called upon the members of the Twelve in order of seniority to express themselves individually as to how they felt about reorganizing the presidency of the Church.

“As each member of the Twelve spoke, he expressed himself as feeling that now was the time to reorganize the First Presidency and that President Spencer W. Kimball was the one whom the Lord wanted to preside at this time. The sweet Spirit of the Lord was present in rich abundance and there was complete unity and harmony in the minds and spoken words of the Brethren. The only purpose and desire was to do the will of the Lord, and there was no question in anyone’s mind but what the will of the Lord had been expressed.

“Elder Ezra Taft Benson then made the formal motion that the First Presidency of the Church be reorganized and that Spencer W. Kimball be sustained, ordained, and set apart as the president, prophet, seer, revelator, and as trustee-in-trust of the Church. This motion was seconded and unanimously approved.”

– N. Eldon Tanner, “Chosen of the Lord,” General Conference, April 1974.

The College of Cardinals is famous for using slips of paper. There’s just no need for them when the Prophet dies.

For a more complete explanation, see comment 17.

When the Prophet dies, the Twelve (i.e. fourteen) go into the temple for inspiration and, once the Spirit gives them a name, they write it down on a piece of paper. If the name is the same on every piece of paper, then that person is considered to have been called by the Lord as the next Prophet.

ME! For #17.

When the President of the Church dies, the Quorum of the First Presidency ceases to exist. That means that the next quorum beneath the First Presidency–the Quorum of the Twelve Apostles–is the presiding quorum of the Church. The senior Apostle is the President of the Quorum of the Twelve. Since he is the President of the presiding quorum of the Church, he really is, already, the President of the Church. No voting required.

The Twelve have the authority (under the direction of their President) to organize a new First Presidency. Since the time of Lorenzo Snow, this has been done rather quickly following the death of the Prophet. But there’s nothing that requires it.

If President Hinckley were to pass away tonight, President Monson, as President of the Quorum of the Twelve, would already be the President of the Church. If he then directed the Twelve to organize a new First Presidency, he would presumably be the President. To me, it’s not inconceivable that the Twelve, under his leadership, could organize a First Presidency with someone else as President. But I doubt very strongly that such a thing will ever happen.