The question of who was to be the true successor to Joseph Smith Jr. was always answered by a story of a meeting of saints where several men gave speaches regarding why they should be the successor and when Brigham Young spoke people thought that Brigham sounded like Joseph Smith Jr. so they voted for Brigham.

This is a nice story, but the problem is that Joseph Smith had legally deteremed who would be the successor and it was ignored.

The below is a transcript of the incorporation of the “Church of Jesus Christ of Latter day Saints” in the state of Illinois by Joseph Smith in Febuary of 1841.

87 City of Nauvoo Hancock Co. Ills
February 2nd A D 1841
To the County Recorder of the County of Hancock
Dear Sir
At a meeting of the “Church
of Jesus Christ of Latter day Saints” at this place on Saturday
the 30th day of January A D 1841. I was elected Sole Trustee
for said Church to hold my office during life (my successors
to be the first Presidency of said Church) and vested with
Plenary Powers as Sole Trustee in Trust for the Church of Latter
Jesus Christ of Latter day Saints to receive acquire manage
or convey property real personal or mixed for the sole use
and benefit of said church agreeably to the provisions of ^ an Act entitled “an
act concerning religious Societies” approved February 6th 1835
Joseph Smith [L.S.]
State of Illinois } ss.
Hancock County } This day personally appeared before me [Daniel]
H Wells a Justice of the Peace within and for the County [of Hancock]
aforesaid, Isaac Galland Robert B Thompson and J[ohn C.]
Bennett who being duly sworn depose and say that [the foregoing]
Certificate of Joseph Smith is true.
Isa[ac Galland]
R. B. [Thompson]
John [C. Bennett]
Sworn to and subscribed this third day of February [in the]
year of our Lord one thousand eight hundred and f[orty-one]
before me Daniel H W[ells]
Justice of the [Peace]

In the event of Joseph’s death, his legal successor was the quorum of the First Presidency. When Joseph died three years later on June 27, 1844, the sole surviving member of the First Presidency was Sidney Rigdon.

Although the rivals who emerged to challenge Sidney — Brigham Young, James Strang, William Smith, David Whitmer and ultimately Joseph Smith III — had inferior succession claims, their leadership was viewed by most of the Saints as much more palatable. Thus we hear the story of Brigham Young and the members choosing him as the successor.

Source = http://www.bycommonconsent.com/