The Taliban's supreme leader, Haibatullah Akhundzada, is expected to have ultimate power over a new governing council, with a president below him, a senior Taliban official told Reuters last month.
The supreme Taliban leader has three deputies: Mawlavi Yaqoob, son of the movement's late founder Mullah Omar; Sirajuddin Haqqani, leader of the powerful Haqqani network; and Abdul Ghani Baradar, one of the founding members of the group.
An unelected leadership council is how the Taliban ran their first government which brutally enforced a radical form of Sharia law from 1996 until its ouster by US-led forces in 2001.
The Taliban have tried to present a more moderate face to the world since they swept aside the US-backed government and returned to power last month, promising to protect human rights and refrain from reprisals against old enemies.
But the United States, the European Union and others have cast doubt on such assurances, saying formal recognition of the new government - and the economic aid that would flow from that - is contingent on action.
The foreign minister of current EU president Slovenia told Reuters the bloc was "far from even tackling this question", which EU leaders might discuss at summits next month. Some EU states consider the Taliban a terrorist organisation.
If the European Union - the world's biggest aid donor - decides to formally recognise the Taliban government, "aid is the leverage that the European Union has" in setting conditions, Anze Logar said.
On Wednesday, U.S. Undersecretary of State Victoria Nuland had said the United States would look at deeds not words.
"So they've got a lot to prove ... they also have a lot to gain, if they can run Afghanistan, far, far differently than they did the last time they were in power," she said.
Humanitarian organisations have warned of catastrophe as severe drought and the upheavals of war have forced thousands of families to flee their homes.
Afghanistan desperately needs money, and the Taliban are unlikely to get swift access to the roughly US$10 billion in assets mostly held abroad by the Afghan central bank.
The Taliban have ordered banks to reopen, but strict weekly limits on withdrawals have been imposed and there are long queues at banks.
"Everything is expensive now, prices are going up every day," said Kabul resident Zelgai.
Afghanistan's real gross domestic product is expected to shrink by 9.7 per cent this financial year, with a further drop of 5.2 per cent seen next year, said analysts in a report from Fitch Solutions, the research arm of ratings agency Fitch Group.
Foreign investment would be needed to support a more optimistic outlook, a scenario which assumed "some major economies, namely China and potentially Russia, would accept the Taliban as the legitimate government", Fitch said.
The new, Taliban-appointed central bank head has sought to reassure banks the group wants a fully functioning financial system, but has given little detail on how it will supply funds for it, bankers familiar with the matter said.
While the Taliban are cementing control of Kabul and provincial capitals, they are fighting with opposition groups and remnants of the Afghan army holding out in mountains north of the capital.
Senior Taliban leader Amir Khan Motaqi called on the rebels in Panjshir province to surrender, saying "the Islamic Emirate of Afghanistan is home for all Afghans", referring to the Taliban-run state.
Opposition leader Ahmad Massoud, son of a former mujahideen commander who fought against the Taliban in northeastern Afghanistan in the late 1990s, told CNN his forces were fighting for a "decentralised state where power is equally distributed between the different ethnic and sectarian groups".
"Unfortunately, the Taliban have not changed, and they still are after dominance throughout the country," he said.