Zardari, Bhutto's widower and co-chairman of the PPP has said that the new president will come from his party, one likely candidate is Aftab Shaban Mirani, Bhutto's former defence minister. Zardari also said it could even be a woman, hinting at his sister Faryal Talpu, who is a member of Pakistan's parliament.
Sharif's party on the other hand wants someone apolitical, perhaps someone from the judiciary. This will prove a major bone of contention between the two major coalition parties, which may start to disintegrate if an agreement cannot be reached within the 30 days given for the process.
According to Rahul Roy-Chaudhury at the London-based think-tank, the International Institute for Strategic Studies, the new president will most likely be a consensual candidate, "not a big charismatic figure or a future player in Pakistani politics." Chaudhury speculates it's likely to be someone from the judiciary or a "has-been politician."
Musharraf's departure signals a major change in Pakistani politics, and whoever succeeds him will not be able to have the same "special relationship" with the United States that Musharraf did.
"Instead of one principal player, you now have four or five," Chaudhury told ABC News.
The United States will now no longer have one go-to person in Pakistan but several. "You'll have Zardari, Sharif, the ISI [Pakistan's Secret Service], the army, the judiciary. ...the multifaceted political dynamics in Pakistan will be more complex than it has been."
The head of Pakistan's army, Gen. Ashfaq Parvez Kayani, who Musharraf installed, has remained largely silent throughout the recent political turmoil but, according to Chaudhury, must have given his nod to the impeachment plans or at least his assurance that he would not interfere with them.
Since Kayani became commander in chief the army has backed away from political involvement, and Kayani has presented himself as more of a soldier's soldier. He has also built up a good relationship with the United States. "While not necessarily a substitute for Musharraf, he is a person the United States is working with," said Chaudhury.
The United States has been nurturing this relationship, as Kayani's role will likely become more important in the campaign against terrorism. America will need his support as head of the army, especially if the critics of the U.S. in Pakistan's government become more vociferous.
Nawaz Sharif, who Musharraf deposed in a 1999 coup, has publicly criticized U.S. policy in Pakistan.
After a recent meeting with the U.S. ambassador to Pakistan, Anne Paterson, Sharif told the media only Pakistanis could decide how to fight militancy.
"I told her that this war, the way you are fighting here, is not in anyone's interest. And we have to look into Pakistan's interests and we don't want our army to fight against the Pakistani state."
But in his speech today, Musharraf argued that he had always done everything for Pakistan's best interests, and that he was leaving a country that has never been more important to the world.
"Before 1999, where was Pakistan? Pakistan had no international identity. Nobody knew Pakistan. We gave Pakistan a status," Musharraf said. "And when we go abroad, there is some weight in our words. We put Pakistan on the map, gave it importance, gave it status, which by the grace of God is still there."