In June of 1844, Joseph Smith, Jr. fell to the bullets of assassins. Thus ended the first phase of the Restoration. Everyone wondered what would happen next and whom they should follow. The Succession Crisis ripped the fledgling church apart. Some ended up following the apostles, who were led firmly by Brigham Young. Some followed James Strang, who produced a forged letter in which Joseph Smith made Strang his successor, and who in many respects hewed more closely to Joseph Smith's model of what a prophet should be. Many who lingered in the Midwest came together to form the Reorganized Church for whom Joseph Smith III became their prophet and president. Others such as Lyman Wight and Alpheus Cutler believed that they had all the authority they needed to carry on the work to which they had been appointed.
In the long run, the so-called Brighamite branch of the Restoration, which migrated to the Salt Lake Basin, became the most numerically successful of the branches. Not infrequently it is this success that is help up as the proof that God had chosen Brigham to carry on His work. The closer one looks at these arguments, however, the flimsier they appear. It is not that the Restoration ended or that priesthood authority suddenly evaporated. Clearly the work was carrying on. What is unclear, however, is the idea that any one of these branches was the only one authorized to continue and that the others were somehow illegitimate. Obviously, some were far more successful than other, but did that make the others wrong or apostate?
Steven Shields (CoC) has long argued to the contrary. He believes that the church Joseph Smith founded cease to exist and that every one of the various groups that would carry on had to do so on a new legal basis, including the LDS Church. Apologists for the LDS Church have cultivated an apostolic claim for their unique basis of legitimacy. Since the bulk of the apostles followed Brigham out west, the LDS Church is the only true Restoration branch. Another way to make the argument is to say that the LDS Church in continuing the ordinances of the temple or plural marriage was the only organization truly to build on the foundation Joseph Smith laid. Of course, any one of these claims can be countered with examples of other groups that did the same, so the LDS position ultimately stands on the claim that the majority of the apostles followed Brigham to Salt Lake. And, this branch has certainly had the greatest numerical and financial success.
Where it concerns priesthood, however, the situation existing at Smith's death did not provide for a clear successor or a monopoly of legitimate authority for any one group, not even the apostles. To the contrary, the priesthood keys were conferred upon many, and those who received these keys through their second anointing occasionally (Lyman Wight, Alpheus Cutler) realized that their authority was sufficient to strike out on their own, much to the frustration of the one man who would come to claim that he was Joseph Smith's successor in every sense, Brigham Young.
I want to suggest that Wight and Cutler were right. They did have all the keys necessary to strike out on their own, and so did everyone else who had been through the second anointing as they had. That would continue to be the case even among those who followed Brigham Young and received their second anointing in Nauvoo before the saints headed west. Of course, this is but one argument that can be made, and it is one that favors the second anointing as a source of complete priesthood authority. Others who had a different idea of priesthood authority felt that they, too, had all of the authority they needed to carry on. All with a reasonable claim should be treated as though they do.