The details have surfaced in a letter written by the boss of the Passenger Rail Agency of South Africa in October 2012.
The letter sets out accusations that the Gupta family and Duduzane schemed to capture the parastatal and grab a R51-billion tender for a bidder they represented.
It state s that , during "numerous meetings", the Guptas, Duduzane and their associates pressured then transport minister Ben Martins and Prasa's then CEO, Lucky Montana, to favour China South Rail to supply the parastatal with 600 commuter trains.
The Guptas, the letter claims, proposed allocating "shares" to Montana and "directly, unashamedly and unapologetically demanded" that Martins restructure Prasa's board.
Montana wrote the letter to then Prasa board chairman Sfiso Buthelezi after discovering that the Department of Transport was preparing a cabinet memorandum to rejig the board.
This week, Montana confirmed that he had written the letter, an unsigned version of which the amaBhungane Centre for Investigative Journalism has seen.
Buthelezi, who did not want to comment on the details, confirmed he had received the letter. And a source close to Martins confirmed the essence of the letter's contents in so far as they relate to him.
The revelations - an unprecedented inside view of how the president's friends allegedly parlay political access into commercial gain - may reopen the wound of ANC secretary-general Gwede Mantashe's failed probe into Gupta "state capture".
The ANC closed the investigation last month after receiving only one written statement.
Montana, who was ousted from Prasa last year over unrelated corruption allegations, said he would "leave for today" why he did not submit a statement.
[We have] the support of the president. [If] you don't work with us, you are not going to get this bid.
The story of the letter starts in September 2012, two months after Prasa issued the train tender. Bids were due by September 30.
"I have previously reported to the chairman," Montana writes, "of my attendance of numerous meetings at various periods with the minister of transport, key advisers in the ministry of transport and representatives of the Gupta family.
"It is in these meetings where I was introduced to representatives of the Gupta family and the son to the president, Mr Duduzane Zuma, and their relationship with one of the bidding companies, China South Railways ... I had taken issue with the representative of the Gupta family over what I considered to be attempts on their part to 'extort' money from [bidders]."
In large engineering contracts, agents who help win tenders are often paid large "success fees".
Montana this week said that he had been called to a first meeting at Martins's Pretoria residence as he was about to leave for a transport conference in Germany in the third week of September.
There, he was introduced to Rajesh "Tony" Gupta, Duduzane and an associate. They indicated their general interest in the tender.
Montana's letter says that at the conference in Germany, bidders told him "that they are required to pay money on the side, that they are aware that the Prasa AGM will be postponed, which truly materialised, and further informed that [the] purpose of the postponement was to allow time for the board of Prasa to be restructured. This will ensure that the requirements of the Gupta family and China South Railways are achieved."
This week Montana said that the bidders told him a Gupta associate had met with bidders in Switzerland, telling them: "We work with Lucky [Montana], we work with Ben Martins [and we have] the support of the president. [If] you don't work with us, you are not going to get this bid."
Montana said he asked for a meeting at the minister's house on his return, where he "blasted" Tony Gupta and Duduzane.
"I thought that was the end of the matter. Unfortunately it was not."
Tony wanted Montana to include two Gupta nominees among the bid evaluators. Their CVs were delivered by a driver. "I rejected that."
The letter continues: "I must also add that the Guptas have presented a plan that I and other people have been allocated shares within CSR, the plan which I rejected contemptuously in the presence of our minister."
Despite my repeated requests to be furnished with a copy [of the letter] in order to respond thereto you refused. Your reasons for refusal are insufficient
And then there were the restructuring attempts. The letter refers to a Gupta associate's direct demand to Martins to restructure the board.
Montana wrote: "I was taken aback and continue to be surprised by the fact that the representative of the said family finds such power, authority and audacity."
On October 28, the letter says, then transport director general George Mahlalela showed Montana "a written memorandum for the appointment of a new chairman and other Prasa directors [that] was being processed for submission to the cabinet".
The next day, Montana met a Gupta associate who "reported that there is agreement at political level that Prasa shall be instructed to cancel the [tender if it is] not awarded to CSR or any one of the other two Chinese bidders".
That is when Montana wrote the letter, threatening to quit. Montana and Buthelezi then met Martins, and the board rejig was averted.
Another bidder, French-backed Gibela, was given the R51-billion contract in December 2012.
China South Rail South Africa representative Wang Pan said this week: "I do not know what you are talking about. I also do not know the people you referred to .. and have never met with them."
Duduzane did not answer calls or respond to text or e-mail messages.
Gupta lawyer Gert van der Merwe said: "Despite my repeated requests to be furnished with a copy [of the letter] in order to respond thereto you refused. Your reasons for refusal are insufficient and ill-considered.
"As a result thereof I advise my clients to reserve their right to comment until you disclose a copy of the document."
Van der Merwe was given the text of the letter but not a scanned copy, due to concerns about protecting its source.