The all-Australian BBHO consortium withdrew its $386 million offer Friday after Gina Rinehart's Hancock Prospecting and its joint venture partner Shanghai CRED increased their bid to acquire the country's largest landholder to $386.5 million.

"We are disciplined investors in Australian rural assets and made what we believed to be a full and fair offer," the consortium said, admitting defeat.

"Each of the BBHO partners wishes the Hancock consortium well and, should they be successful in completing the acquisition, we look forward to welcoming them as neighbours."

The Hancock bid pipped BBHO's offer by $500,000.

BBHO was made up of four of Australia's wealthiest farming families, the Buntine, Brinkworth, Harris and Oldfields.

They own substantial landholdings in the Northern Territory, Queensland, South Australia and New South Wales and intended to divvy up the Kidman properties between themselves, using the iconic S. Kidman & Co as a brand name only.

The individuals involved were unsentimental about withdrawing, a source close to the consortium said.

Mustering cattle, working with rams

Sterling Buntine was mustering cattle on his stations and Tom Brinkworth was working with rams in the Riverina. "They're moving on," they said.

The consortium said it had gained a "very strong groundswell of public support ... from well-wishers across the country, all of whom recognise the importance of the Kidman name and legacy to our industry."

The Kidman company is Australia's largest private landholder.

It controls 100,000 square kilometres of pastoral leases and 185,000 head of cattle across Western Australia and the top end to South Australia.

The Hancock and Shanghai CRED's joint venture, known as Australian Outback Beef, lodged takeover-bid documents with the Australian Securities and Investments Commission on Thursday following a recommendation by the Kidman board.

The new offer strengthens Ms Rinehart's hand, but a higher wild-card bid could still derail the takeover before the offer period ends on December 9.

The Hancock joint venture must get approval from Australia's Foreign Investment Review Board and the Chinese government to be successful.

It also needs various state governments to approve the transfer of leases which make up nearly all the landholdings.

But Ms Rinehart has said Hancock will fully fund the purchase and go it alone if the joint venture is knocked back by Treasurer Scott Morrison, who has already twice rejected sales of Kidman.

"I stand behind the bid and should FIRB or [Chinese] approvals not be achieved, then Hancock will proceed with the acquisition on a 100 per cent basis," Ms Rinehart said on Thursday.