By BBC World Service
Nigerian groups are lobbying for the post of vice-president after Goodluck Jonathan was sworn in as president following the death of Umara Yar'Adua.
Whoever is named vice-president could be a strong contender for presidential elections due in 2011, analysts say.
It remains unclear whether Mr Jonathan will seek to stand for the governing People's Democratic Party.
There is no deadline for him to name a new deputy but an announcement is expected within the coming days.
Many shops and business in Nigeria remain closed as the seven days of official mourning continue.
But the BBC's Caroline Duffield in the capital Abuja says politics ticks on - over the phone and in private meetings.
Nuhu Ribadu - former anti-corruption chief
Aliyu Gusau - newly appointed national security advisor
Alhaji Yayale Ahmed - cabinet secretary
Sule Lamido - governor of Jigawa state
David mark - president of the senate
Murtala Yar'Adua - late president's nephew
She says there are still no answers to the big questions about Nigeria's future.
The political deal that has traditionally ensured peace between north and south is coming under strain, our correspondent says.
The PDP has a tradition of alternating power between the mainly Muslim north and the largely Christian south.
Mr Jonathan is a southerner and Mr Yar'Adua died less than half-way through the north's "turn" of two presidential terms.
To maintain regional balance, Mr Jonathan would be expected to name a northerner as his deputy, which could put that person in a strong position to contest the elections due early in 2011 on behalf of the PDP.
However, there is strong speculation that Mr Jonathan may seek to defy political convention and stand himself.
Thousands at funeral
Tens of thousands of men shoved and pushed their way into the stadium in Katsina to pay their respects to Nigeria's later President Umaru Yar'Adua.
Chants of "Allahu Akbar" (God is great) began as his body - on a bamboo stretcher and wrapped in a Nigerian white and green flag - was carried in by military men.
Former military ruler Muhammadu Buhari and Ibrahim Babangida were among the mourners. Other dignitaries included Niger's interim prime minister. There was also a government delegation, but Mr Yar'Adua's deputy, newly sworn-in President Goodluck Jonathan, was not among them.
Security was tight during the prayers, which lasted about 30 minutes in the 40 degree heat; and the mood was sombre as the body was removed to the cemetery for a burial mainly attended by those close to the late president.
Mr Jonathan has been acting president since February and will serve out the rest of the current presidential term.
Mr Yar'Adua died on Wednesday in the capital Abuja.
Thousands attended the funeral in his home town of Katsina.
Mr Yar'Adua's election in 2007 marked the first transfer of power from one civilian president to another since Nigeria's independence in 1960.
He promised a string of reforms in Africa's most populous nation, including tackling corruption and reforming the inadequate energy sector and flawed electoral system.
Analysts say he made the most progress in tackling unrest in the oil-rich Niger Delta by offering amnesties to rebels.
His long absence and the lack of detailed information about his health led to a political limbo in Nigeria, which was only filled when Mr Jonathan was named as acting president.
However, there was constant tension between supporters of Mr Yar'Adua and Mr Jonathan and in March the acting president dissolved the cabinet and later put his own team in place.
During Mr Yar'Adua's absence, Nigerian Nobel prize-winning author Wole Soyinka was involved in the campaign to resolve the power vacuum.
On Thursday he said Mr Yar'Adua's illness had been manipulated by politicians who had concealed the fact he was in a vegetative state while making arrangements for the forthcoming election.
He told the BBC the late president had been a victim of a macabre game over his succession and not been allowed to be ill in dignity-BBC World Service