The absence of a strong political opposition or free media means any eventual transition of power is likely to be decided within a close circle of Karimov`s family and top officials.
"At the moment, it is too early to make any forecasts about his condition in the future," his daughter Lola Karimova-Tillyaeva wrote on her Instagram page on Monday. "I will be grateful to everyone who will support my father with prayers.
The government of Central Asia`s most populous country, with reserves of oil, gas and gold, said on Sunday Karimov was undergoing hospital treatment, but gave no details.
A failure to reach consensus on a transition could destabilize a mostly Muslim nation of 32 million long targeted by Islamist militants and strategically located north of Afghanistan, in the resource-rich region where Russia, China and the West vie for influence.
Since Uzbekistan became independent with the 1991 collapse of the Soviet Union, Karimov has with some success courted both the West and Russia as well as China, maintaining political and economic links with all.
ANDIZHAN RIOTS
Karimov has been criticized by rights groups and some governments over his human rights record, but argues the country is at risk of becoming a conduit for Islamist militants from Afghanistan to Russia and western Europe. The Uzbek government has accused Islamists of being behind protests in the city of Andizhan where police and security forces fired into a crowd in 2005, killing 187 people, according to official reports.
Karimov has no sons, who might have been regarded as heirs apparent in the patriarchal culture. His elder daughter, Gulnara, has not appeared in public since several media reported in 2014 that she had been placed under house arrest.
Karimov`s second daughter, Lola, is Uzbekistan`s ambassador to Paris-based UNESCO.
Among Uzbekistan`s ex-Soviet neighbors, only Turkmenistan, a more wealthy gas exporter with a much smaller population, saw a relatively smooth transition when its Soviet-era leader Saparmurat Niyazov died in 2006. Kurbanguly Berdymukhamedov, then deputy prime minister, took over.
Poorer Kyrgyzstan, on the other hand, has gone through two violent revolutions accompanied by ethnic clashes. Another neighbor, Tajikistan, went through a devastating civil war in the 1990s after Soviet institutions crumbled.
Some of those who fought against the Tajik government at the time were members of the Islamic Movement of Uzbekistan, a group which has been outlawed at home and has pledged allegiance first to the Taliban and then to the Islamic State.
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