British expats who want Brexit to be halted because of "corrupt practices" during the 2016 referendum have had their case heard in the High Court.
The UK in EU Challenge group says the result should be quashed because of "misconduct" by pro-Leave campaigners.
Mr Justice Ouseley's decision is expected on either Monday or Tuesday.
An earlier attempt to challenge the result was rejected on the grounds that it had not been proven that any wrongdoing affected the vote's outcome.
The case is being brought against the government by four British citizens living on the European continent, Susan Wilson, Elinore Gayson, Carole-Anne Richards and John Shaw.
They say the Article 50 process, by which the UK is leaving the EU, should be halted due to breaches of spending limits and other irregularities by leave-supporting groups during the referendum.
Lawyers for the group say the infractions, which resulted in Vote Leave and Leave.EU being fined £61,000 and £70,000 respectively by the Electoral Commission earlier this year, cast doubt on the legitimacy of the result under the terms of the 1983 Representation of The People Act.
Speaking after the hearing, Susan Wilson said she was hopeful of success.
"We also maintain our firm belief that the referendum result cannot be considered the 'will of the people'," she said.
"The Leave campaign's fraudulent behaviour has been proven by the Electoral Commission and we are continually frustrated that the government fails to acknowledge the impact of this illegality and continues to defend its position."
The campaigners' written arguments were dismissed at a preliminary hearing in September, when Mr Justice Supperstone ruled that the electoral watchdog, in punishing the two leave campaigns, had not established that the referendum result had been "procured by fraud".
Friday's oral hearing enabled the group to make their case in person.
If he decides to grant a judicial review, the campaigners have asked for it be expedited, saying it is a "matter of urgency" the matter is dealt with before the UK's scheduled departure on 29 March 2019.
Government lawyers say Theresa May did not act unlawfully when she triggered Article 50 in March 2017, since that although the Electoral Commission investigations were a matter of public record at the time, their findings that campaign violations had occurred were not known until over a year later.
They also argue there is no evidence of a "causal effect" between breaches of campaign rules and the outcome of the referendum - which saw a 51.9% to 48.1% vote in favour of leaving the EU.
The prime minister has said the referendum was the biggest democratic exercise in UK history, with more than 33 million people taking part, and it is her duty to implement the peoples' wishes.
The official remain campaign, Britain Stronger in Europe, was fined £1,250 last year for not declaring certain invoices correctly while the Liberal Democrats, which backed staying in the EU, were fined £18,000 for not providing acceptable invoices or receipts for 80 payments.
In a separate case, the European Court of Justice will rule on Monday whether the UK has the right to unilaterally rescind Article 50 without the say-so of the EU's 27 other members.