If he fails and Mr Malema emerges victorious, that will be the end of Mr Zuma's authority both within and without the ANC.
Parliament would elect Mr Mbeki's successor and Kgalema Motlanthe, an ally of Mr Zuma and the deputy leader of the party, is now touted as the likely caretaker.
But the ANC's leaders are probably strong enough to resist firebrands such as Julius Malema, the leader of the party's Youth League and a strident supporter of Mr Zuma, and so should be able to keep the party together for now.
The court's judges had earlier accused John Hlophe, a controversial judge who presides over the high court in the Western Cape, of trying to lean on two members of the constitutional court to persuade them to rule in favour of Mr Zuma.
Unless, of course, Mr Zuma resigns of his own accord - and at the moment, no one is putting any money on that.
South Africa sent 200 troops in January out of a planned deployment of 400, Mr Zuma said.
On Tuesday the Durban High Court confirmed the withdrawal of charges against Mr Zuma, but explained that this was not the same as an acquittal.
ECONOMIST: Jacob Zuma is poised to become president of South Africa
But that theory was quickly shot down in flames by a squadron of hacks keen to point out that Mr Zuma - a man of great personal charm who can also wow a crowd with his singing and dancing - is simply not much of a wordsmith and that no grander conclusions should be drawn.
"We can boast that we're a leader of our society, that therefore we have something to contribute to the democratic life of this country, to this democratic Republic of South Africa, " Mr Zuma said after his win.
She will hold a number of bilateral meetings, including with the President of the 67th Session of the UN General Assembly Mr Vuk Jeremic, Dr Nkosazana Dlamini Zuma, new chair of the African Union, and Ms Leila Zerrougui, UN Special Representative for Children and Armed Conflict.
"Because the ANC is so dominant (in South Africa), it sends the message to people that if they want power, they can gain it through intrigue and if they succeed they will, of course, try to retain it through intrigue, " Mr Matshiqi says, lamenting the ugly nature of the Zuma-Mbeki battle.
Our correspondent says it is now difficult to see how Mr Malema can affect the ANC leadership contest next year, but Mr Zuma is not certain of a second term and other critics remain.
In his statement released on Sunday evening, Mr Zuma thanked "the thousands of South Africans who prayed for Madiba at various Easter church services".
Like many liberation fighters, Mr Zuma was once a member of the SACP, but quit in 1990 and went on to give his full backing to Mr Mbeki's market-friendly economics.
Samuel Manetoali, the First Lady of South Africa, Mrs Sizakele Zuma and the Former President of the Republic of Cap-Vert, Mr Antonio Manuel Mascarenhas Gomes Monteiro.
Mr Zuma looked set to become president of South Africa after the 2009 parliamentary elections, but the corruption allegations persisted.
Mr Malema, 30, wants Mr Zuma replaced as party leader ahead of the 2014 elections and replaced with deputy leader Kgalema Motlanthe.
But President Mandela and Mr. Zuma the likely next leader of the country, the trade unions and other civil society leaders who've already spoken out very clearly, so at this point President Mbeki appears pretty isolated within South Africa.
Mr Zuma is expected to sign a series of trade agreements with his country's largest trading partner.
Mr Zuma still cites land reform as one of his five top priorities.
Mr Zuma, who was acquitted last year of rape charges which he said were politically motivated, may still face corruption charges.
Mr Zuma said infrastructure was at the heart of one of the key issues for the continent, namely how Africa leads itself.
In response, the ANC said in a statement that the party was "increasingly disturbed" by the manner in which the former archbishop of Cape Town was addressing the issue before an announcement on whether Mr Zuma's trial would proceed.
Mr Malema's Youth League, who helped Mr Zuma come to power, are keen to deprive him of the second term he desperately wants.
But Mr Zuma also went much further - explicitly questioning the right of journalists and others to probe the state on matters of security.
Mr. Zuma isn't a stranger to hardball politics ahead of elective conferences.
Candidates for three of the top four jobs were elected unopposed: Mr Mbeki as president, Jacob Zuma as his deputy, and Kgalema Motlanthe as secretary-general.
Mr Mandela was admitted to hospital just before midnight, the office of President Jacob Zuma said earlier.
Born to a Zulu family in 1942, Mr Zuma has spent his entire adult life since 1959 in the service of the ANC.
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