Mormon Newsroom shared the following about how succession to the presidency of the Church takes place after a prophet's passing. We honor President Monson and will greatly miss him.
The appointment of a new president of the Church happens in an orderly way that — remarkably in today’s world — avoids any trace of internal lobbying for position or rank. Viewed by members as a divinely revealed process, it is devoid of electioneering whether behind the scenes or in public.
Moreover, it is not only the structure of Church organization that governs this process. There is also a deeply ingrained tradition in the Church that personal aspiration for leadership at any level is inappropriate. Instead, the emphasis is on personal worthiness and a humble willingness to serve when invited.
When the president of the Church passes away, the following events take place:
1. The First Presidency is automatically dissolved.
2. The two counselors in the First Presidency revert to their places of seniority in the Quorum of the Twelve Apostles. Seniority is determined by the date on which a person was ordained to the Twelve, not by age.
3. The Quorum of the Twelve Apostles, now numbering 14 and headed by the senior apostle, assumes Church leadership.