The High Court challenge to the election of former Family First senator Bob Day has ended in an acrimonious battle over costs, with the court reserving its decision.

The court was asked by the Senate to consider whether Mr Day may have breached the constitution in the lease arrangements for his office.

The case is focused on who owned a building in Kent Town, South Australia, where Mr Day set up his electorate office.

In the hearing's final hours on Tuesday afternoon, lawyers for former South Australian Labor senator Anne McEwan and the Commonwealth locked horns over whether she was entitled to compensation for her part in the case.

Ms McEwen, who lost her position in the 2016 election, is one of several defeated candidates in the running to replace the now-retired Family First senator.

But her bid to widen the scope of the case was rejected by the High Court last month.

Lawyers for Ms McEwen had hoped to convince the court Mr Day retained controlling ownership of a building from which the Commonwealth leased his electorate office.

But Justice Michelle Gordon rejected the idea and said she thought it was likely Mr Day believed he had followed the rules to be eligible for election.

Today the Commonwealth argued Ms McEwen had not added much to the case and did not merit an order for costs.

Her lawyer Jeremy Kirk countered saying: "She's the one with skin in the game."

Decision delayed due to complexity of case

The High Court had hoped to resolve the case soon after it was referred by the Senate, but was delayed by the complexity and the number of parties.

The court even took the unusual step of taking evidence from witnesses at a special hearing in Melbourne.

The court, sitting as the Court of Disputed Returns, was asked to consider two issues; whether Mr Day breached the constitution in the lease arrangements for his office, and if he did, how his Senate seat should be filled.

The dispute revolves around whether Mr Day had an interest in the building housing his electorate office. ( ABC News )

The constitution bans parliamentarians from having a direct or indirect pecuniary interest in any arrangement with a Commonwealth.

The Solicitor-General and Ms McEwan argued, at the very least, there was an indirect perception that Mr Day had a pecuniary interest in the lease arrangement.

Mr Day had been told by the Senate he could not lease an office in a building he owned.

He responded by transferring the property to Fullerton Investments, which was to be run by a friend, with benefits to the Day Family Trust.

The man running Fullerton Investments then nominated a bank account in the name of Fullerton Nominees, which was controlled by Mr Day, to receive rent payments.

Mr Day's lawyer told the court his client had nothing to do with that decision, or other arrangements made independently without his direction, by others including his accountant.

The court heard there was no evidence Mr Day had any expectation of receiving any money.

But Ms McEwan's lawyer told the court despite the transfer of the property, Mr Day retained an interest which had a financial benefit.

"The whole purpose was to house the property so Mr Day could receive the rental allowance," Mr Kirk said.

Day's high profile 'distorted' number of Family First votes

Mr Kirk also argued any recount should omit some of Mr Day's votes, because his high profile had distorted the result.

But Commonwealth Counsel Neil Williams sided with Mr Day on the issue.

"The disqualification of a person on the ballot paper does not invalidate the ticket or the vote," he said.

Mr Williams said there was no basis to disregard nearly 25,000 votes for Family First.

The court has reserved its decision on all issues, including costs.