The court said that it would now deliberate on the details and deliver a judgement in a timely manner, expected in the coming weeks.
The government is persuing extradition of Mallya and Modi from the UK while Choksi is believed to be in Antigua and Barbuda
The extradition was upheld but he is still here because as you know there is another route for him to apply to the Secretary of State for status, said barrister Philip Marshall.
The 65-year-old businessman, whose legal challenge to the Indian government's extradition request was turned down at the Supreme Court level in the UK last year, remains in Britain on bail.
Solicitor General Tushar Mehta shared a letter of the Ministry of External Affairs' official Devesh Uttam written to him on the status of extradition of Mallya from the United Kingdom.
Mallya left the country in March 2016 for the United Kingdom where he is legally contesting the extradition ordered by the British Government.
The hearing forms part of a series being heard by the High Court since the SBI-led consortium of 13 Indian banks had initiated the proceedings against Mallya.
The 65-year-old former Kingfisher Airlines chief seeks approval to use 2.8 million pounds of the estimated 2.9 million pounds held by the court under the UK's Insolvency Act 1986.
The depositions left no time for closing submissions in the case, which has now been adjourned to a yet-to-be-agreed date in the New Year.
Vijay Mallya's counsel, Philip Marshall, had argued that his client needed urgent access to the substantial funds held by the court to cover his living and legal expenses.
The latest seizure of Mallya’s overseas assets comes as India awaits the extradition of the 64-year-old former MP from the UK. Mallya is wanted for defaulting on loans worth up to Rs 9,000 crore.
Mallya lost his appeals in the UK Supreme Court against his extradition to India to face money laundering and fraud charges.
Mallya had cited the poor condition of the jails in India to avoid extradition and possibility of being lodged at this jail.
A counsel for Mallya appeared in the court on last Monday, as per the scheduled date of hearing, and sought some documents, officials said.
Rahul Gandhi says Indian prisons 'difficult places' but Vijay Mallya shouldn't be treated differently
Mallya last month appeared before a court in London where both defence and prosecution presented clarifications on Barrack 12 at Arthur Road Jail in Mumbai, where Mallya is to be held.