Prophet Muhammed Did Not Apoint A Khalif
Commonly amongst the Sunnis it is believed that Prophet of Allah appointed Abu Bakr Sadeeq radiallah tallah anh as his 1st Khalifah. And Shia Rawafiz are of beleife that Ali radiallah tallah anh was apointed as the 1st Khaleef, but the evidence points contrary to both believes.
Narrated by Al Aswad, who stated that Um Ul Momineen Aysha Sadeeqah radiallah tallah anha, had negated Ali radiallah tallah anh being apointed as the 1st Khalifah of RasoolAllah:
* Sahih Bukhari, Book 59, Number 736: “Narrated Al-Aswad: It was mentioned in the presence of 'Aisha that the Prophet had appointed 'Ali as successor by will. Thereupon she said, "Who said so? I saw the Prophet, while I was supporting him against my chest. He asked for a tray, and then fell on one side and expired, and I did not feel it. So how (do the people say) he appointed 'Ali as his successor?"
* Sahih Bukhari, Book 51, Number 4: “Narrated Al-Aswad: In the presence of 'Aisha some people mentioned that the Prophet had appointed 'Ali by will as his successor. 'Aisha said, "When did he appoint him by will? Verily when he died he was resting against my chest (or said: in my lap) and he asked for a wash-basin and then collapsed while in that state, and I could not even perceive that he had died, so when did he appoint him by will?"
* Sahih Muslim, Book 13, Hadith 4013: “Aswad b. Yazid reported: It was mentioned before A'isha that will had been made (by the Holy Prophet) in favour of 'Ali (as the Prophet's first caliph), whereupon she said: When did he make will in his favour? I had been providing support to him (to the Holy Prophet) with my chest (or with my lap). He asked for a tray, when he fell in my lap (relaxing his body), and I did not realise that he had breathed his last. When did he make any will in his ('Ali's) favour?”
This also indicates that if Ali radiallah tallah anh was apointed as the1st Khalifah on any another ocasion then she would have known it, and the Sahabah as whole would have known this.
Infact Prophet of Allah did not make a will in which he nominated a Khalifah or a will in which he passed mentioned distribution of inheritance:
* Sahih Bukhari, Book 61, Number 540: “Narrated Talha: I asked 'Abdullah bin Abi 'Aufa, "Did the Prophet make a will (to appoint his successor or bequeath wealth)?" He replied, "No." I said, "How is it prescribed then for the people to make wills, and they are ordered to do so while the Prophet did not make any will?" He said, "He made a will wherein he recommended Allah's Book."
From:
http://www.islamimehfil.com/topic/22953-hazrat-abu-bakr-first-khalifah-of-prophet-sallallahu-alayhi-wa-aalihi-wassallam/(I checked all narations and they are correctly referenced)