The strangest US presidential campaign in recent memory now includes a social media spat between its two most famous TV businessmen. In the blue corner: ABC’s Shark Tank celebrity investor Mark Cuban. In the red: the one and only former emcee of NBC’s The Apprentice, Donald Trump.

The two, and their surrogates, have been at it for months. But the latest spat, over the Republican nominee’s proposed border wall with Mexico and detention centers for undocumented immigrants, comes amid on/off rumors that Cuban might act as a surrogate for Trump during Hillary Clinton’s preparation for their first presidential debate.

Perhaps that’s why Cuban has taken to trolling Trump for details on his plans. For all his bluster about the wall, Cuban noted, Trump hasn’t provided any architectural or financial infrastructure for the project that has been the cornerstone of his campaign for the highest office in the land.

.@realDonaldTrump this is a real request. Can you publish renderings of the wall and it's placement on our southern border. I'll pay 4 them — Mark Cuban (@mcuban) September 1, 2016

There’s also the matter of funding – is Trump proposing new federal government agencies? State government agencies in Cuban’s beloved Texas? How would the deportation process work?

We just heard @realDonaldTrump's infrastructure prog. .A wall. Detention centers.Thousands of new gov emps to find, evaluate,process,deport — Mark Cuban (@mcuban) September 1, 2016

The owner of the Dallas Mavericks also went after the Republican presidential nominee over taxes this week. On Wednesday, he unleashed an unusually well-researched tweetstorm about his suspicions regarding Trump’s tax returns, observing from trial depositions that the Republican uses limited liability companies very liberally in his construction businesses.

2) Trump states in his attached deposition that he uses Sub Chapter S corporations for his development projects. pic.twitter.com/gNDbTgGxrw — Mark Cuban (@mcuban) August 31, 2016

So far Cuban has not managed to needle Trump into a reply. But his spokesman, Michael Cohen, has risen to the task, accusing Cuban’s supporters of being “paid trolls” who were “ruining legitimate discussions”, apparently drawing a salary from Cuban:

Cuban denied the charges, questioning, as he had with Trump’s proposed wall, whether Cohen could provide any logistical details for the process of paying a troll to harass someone on Twitter.

I wouldn't know how to pay trolls. Can you explain to me how it's done? https://t.co/zL8QTFVGXE — Mark Cuban (@mcuban) September 1, 2016

Then Cuban felt the need to twist the knife: had Cohen been told “you’re fired”? “People are saying” Cohen had left the campaign, Cuban wrote using a favorite Trump construction.

I don't need a job. I can be on here all I want. Do you still have a job with DJT? People are saying you got fired https://t.co/mndw9DkEhC — Mark Cuban (@mcuban) September 1, 2016

No, said Cohen. But he did ask if Cuban was looking for a new lawyer.

.@mcuban @RamieEgan absolutely untrue...feel free to call me in the office to confirm. Are you hiring? — Michael Cohen (@MichaelCohen212) September 1, 2016

Shark Tank returns to ABC on 23 September. The first presidential debate is on 26 September. Celebrity Apprentice returns on 2 January with former California governor and action-movie star Arnold Schwarzenegger as its host.