There were heated exchanges in the chamber last night as members of the Northern Ireland Assembly voiced opposition to a determination from Mr Trimble and Mr Mallon for the appointment of two junior ministers to help with the "remarkable burden" carried by their central office.
Representatives from the DUP, Sinn Fein and the smaller parties outlined their concerns that the Ulster Unionists and the SDLP were playing party politics and carving up positions.
This charge was rejected by the First and Deputy First Ministers, and their proposal was later carried by 49 votes to 38 after a lobby vote.
Tabling an amendment, which was later defeated in a lobby vote, Mr Nigel Dodds, the DUP MLA for north Belfast, called for the decision to be overturned because the central office already had six paid advisers at its disposal.
"We're going to be in Northern Ireland the most over-governed part of Europe or Western democracy that is possible to imagine, given the number of ministers, junior ministers, Assembly members, councils, quangos and the rest," said Mr Dodds.
Mr Trimble said the two posts needed to be filled as a matter of urgency because of "the remarkable burden we need to carry". The passing of the determination now means the appointments must be made within the next seven days.
Mr Mallon said the appointments were necessary because the issues under the remit of the central office, which include economic policy, the equality unit, the civic forum, community relations, European affairs, victims and women, should not be allowed to suffer if he and Mr Trimble were focused on the wider issues.
It is proposed that the two junior ministers would take control of the economic unit and the equality agenda under the supervision of the First and Deputy First Ministers, although the precise roles to be filled were not specifically outlined in yesterday's determination.
Mr Dermot Nesbitt, the Ulster Unionist party senior negotiator, has been tipped to take the junior ministry with responsibility for economic policy while last night speculation still surrounded which SDLP Assembly member would take control of the equality unit.
Mr Alex Attwood, MLA for West Belfast, Mr Denis Haughey, MLA for Mid Ulster, and Mr Alban Maginness, MLA for North Belfast, have all been connected to the post.
According to Mr Mallon, the UUP and SDLP wished to nominate members of their own parties because they would have to have full confidence in them. He added that additional junior ministerial positions could be created at a later stage for the other departments.
Mr Dodds highlighted that Mr Mallon and Mr Trimble were from different parties yet could work together.
The Sinn Fein MLA for Foyle, Mr Mitchel McLaughlin, said his party had always argued that the central office was top-heavy with responsibility, and the issues should have been spread more evenly throughout the departments from the beginning.
He said the UUP and the SDLP had forgone an opportunity to set aside party political interests and had chosen to create a closed shop.
Sinn Fein voted against the determination along with the DUP, Women's Coalition, Progressive Unionist Party and the other anti-agreement unionist Assembly members. The Alliance party abstained. Mr David Ford, of the Alliance party, described the wording of the determination as vague.
"Confidence isn't exactly brimming over in this chamber, and people want their friends beside them," he added.
The PUP's Mr Billy Hutchinson, MLA for North Belfast, said the new positions should work across the departments rather just within one. He called for the creation of a junior ministry for children.
"If we are going to make an impact here we are going to have to make sure we are putting people in positions that are going to work," he said.
The extra remuneration for the junior ministers was highlighted by Ms Monica McWilliams of the Women's Coalition, who said the Assembly expected a job description because the new appointees would receive a salary of £55,300 a year.
During a direct exchange between the SDLP's Mr Alban Maginness and Mr Ian Paisley jnr, the DUP MLA for east Antrim, Mr Maginness criticised the two DUP ministers for appointing two private parliamentary secretaries without approval from the Assembly.
Mr Paisley, who had accused the SDLP of being "party to corruption" and of creating "jobs for the boys" with the UUP, said the new posts with the DUP were being financed by its central party fund.
Mr Cedric Wilson, the leader of the Northern Ireland Unionist Party, said the two larger parties were attempting to create a "cartel".
He advised the Speaker, Lord Alderdice, to "fix yourself very firmly in your seat" as the two parties might soon want his job.
Closing the debate, Mr Mallon criticised a number of the MLAs who had spoken against the motion.
"I can think of some people in the DUP that I would not put in charge of children's issues or women's issues," he said.
Mr Mallon speculated that the same "pontificating and self-righteousness" would not have been evident during yesterday's debate if the proposals had been for the creation of junior ministries in all 10 departments.