Further to appointing Shoghi Effendi as “the Guardian of the Cause of God,” ‘Abdu’l-Bahá’s Will and Testament established the Guardianship as a hereditary institution: “after him [Shoghi Effendi] will succeed the first-born of his lineal descendents.” The Will and Testament set forth specific conditions for Shoghi Effendi’s appointment of his successor:

0 ye beloved of the Lord! It is incumbent upon the Guardian of the Cause of God to appoint in his own life-time him that shall become his successor, that differences may not arise after his passing. He that is appointed must manifest in himself detachment from all worldly things, must be the essence of purity, must show in himself the fear of God, knowledge, wisdom and learning. Thus, should the first-born of the Guardian of the Cause of God not manifest in himself the truth of the words:—”The child is the secret essence of its sire,” that is, should he not inherit of the spiritual within him (the Guardian of the Cause of God) and his glorious lineage not be matched with a goodly character, then must he, (the Guardian of the Cause of God) choose another branch to succeed him.

The Hands of the Cause of God must elect from their own number nine persons that shall at all times be occupied in the important services in the work of the Guardian of the Cause of God. The election of these nine must be carried either unanimously or by majority from the company of the Hands of the Cause of God and these, whether unanimously or by a majority vote, must give their assent to the choice of the one whom the Guardian of the Cause of God hath chosen as his successor. This assent must be given in such wise as the assenting and dissenting voices may not be distinguished (i.e., secret ballot).

As these provisions of the Will and Testament make clear, ‘Abdu’l-Bahá specified several requirements for the Guardian’s appointment of his successor:

1. It is “incumbent upon the Guardian of the Cause of God to appoint in his own life-time him that shall become his successor…
2. The appointee “must manifest in himself detachment from all worldly things, must be the essence of purity, must show in himself the fear of God, knowledge, wisdom and learning.”
3. “[A]fter him [Shoghi Effendi] will succeed the first-born of his lineal descendents.”  Should “the first-born of the Guardian of the Cause of God. . . not inherit of the spiritual” and not possess “a goodly character,” then must the Guardian “choose another branch” (male descendent of Bahá’u'lláh) “to succeed him.”
4. “The Hands of the Cause of God must elect from their own number nine persons…”
5. And these nine elected Hands “must give their assent to the choice of the one whom the Guardian of the Cause of God hath chosen as his successor.”

Thus, ‘Abdu’l-Bahá specified who could appoint the Guardian’s successor (Shoghi Effendi could); when the appointment was to be made (in Shoghi Effendi’s lifetime) what spiritual qualities the successor had to possess (detachment, fear of God, knowledge,etc.); who the successor could be (Shoghi Effendi’s “first born” or another “branch”); and who had to approve the choice of the successor( nine elected members from among the Hands of the Cause of God). Each of these conditions had to be satisfied for an individual to become Shoghi Effendi’s successor.

By the time of his passing in 1957, Shoghi Effendi had not, however, appointed a successor. The appointment of a successor was made impossible because Shoghi Effendi did not have any children and, therefore, no “first-born” child; nor was there another :”branch” (male descendent of Bahá’u’lláh) eligible for appointment inasmuch as all had broken the Covenant. Moreover, the other conditions for the appointment of a successor had not been satisfied: Shoghi Effendi had not “in his own life-time” appointed a successor who had “inherit[ed] of the spiritual”; and the Hands of the Cause had not “elect[ed] from their own number nine persons” who had given “their assent to the choice of the one whom the Guardian of the Cause of God hath chosen as his successor.” Thus the requirments for the appointment of a successor, as delineated in the Will and Testament of ‘Abdu’l-Bahä, could not be satisfied.
Shahin Vafai, The Essence of the Covenant, p. 83-85

As to the appointment of a successor, the Master had stated in His Will and Testament that should the ‘first-born’ of the Guardian not inherit his spiritual qualities, he should appoint another Ghusn (Branch). The word Ghusn has been used by Bahá’u'lláh to signify His male descendants exclusively. ‘Abdu’l-Bahá was designated as  Ghusn-i-A’zam (The Most Great Branch) and Shoghi Effendi as Ghusn-i-Mumtaz (The Chosen Branch). Shoghi Effendi was not in a position to appoint a successor to himself because he had no son and there was not a single Ghusn who was faithful to the Cause of God. Every one of the descendants of ‘Abdu’l-Bahá had been declared a Covenant-breaker.
Adib Taherzadeh, The Covenant of Bahá’u’lláh, p. 378