With the succession of president Hinckley's presidency immanent, the following BYU Studies article by Ronald Walker sheds some light on the development of the succession process and earlier difficulties before the tradition became established.
Events during 1887‒89, during Elder Wilford Woodruff's succession to the Presidency of The Church of Jesus Christ of Latter-day Saints, remains an important but largely untold story—a time when differing views divided the Church's General Authorities and when the policies and procedures for installing a new president of the Church ere tested and confirmed. These years are also important for the insights they offer in understanding the life of Heber J. Grant, who himself regarded that time as a personal watershed. While it is clear that he acted with candor, energy, and idealism throughout the episode, with hindsight he believed that he had erred, especially in breaching a vital rule of the Quorum—collegiality—as he and other young members of the Twelve had tried too hard to make their views prevail. So deep his later anguish, he cut troubling passages from his diary, and on becoming a senior Church leader he either avoided speaking of the Woodruff episode or retold the incident without including much of its detail, a not altogether conscious handling of a painful memory. But clearly it was a lesson learned. For the rest of his life, unity among the "Brethren" was a cherished, if never fully realized, ideal.
Read the article here.