Julian Assange will learn if he is to be extradited to Sweden to face sex crime allegations.
Lawyers for the WikiLeaks founder are asking the UK's highest court to block his removal, arguing that the European arrest warrant issued against him is "invalid and unenforceable".
A panel of seven Supreme Court judges, who heard the case in February, will give their judgment and end a marathon battle in the UK courts over the issue on Wednesday.
Julian Assange will learn if he is to be extradited to Sweden
The Swedish authorities want Assange, 40, to answer accusations of raping one woman and sexually molesting and coercing another in Stockholm in August 2010 while on a visit to give a lecture.
Assange, whose WikiLeaks website has published a mass of leaked diplomatic cables that embarrassed several governments and international businesses, says the sex was consensual and the allegations against him are politically motivated.
In November 2011, the High Court upheld a ruling by District Judge Howard Riddle - who sat at Belmarsh Magistrates' Court, south London, in February 2011 - that the Australian computer expert should be extradited to face investigation.
If the Supreme Court rejects his appeal it will mark the end of his lengthy legal battle in the UK, but it will still be open to him to ask the European Court of Human Rights in Strasbourg to intervene.
Special arrangements are being made by the Supreme Court for today's ruling because of the worldwide interest of press and media in the judgment.
The High Court declared that it would not be unfair or unlawful to extradite Assange.
But his QC argued in the Supreme Court that the Swedish public prosecutor who signed the arrest warrant could not issue a valid document because she lacked impartiality and independence.
Assange, who is on bail living with friends, attended the two-day hearing in person.
Dinah Rose QC, for Assange, said his latest appeal raised the single issue of law as to whether the Swedish public prosecutor constituted a "judicial authority" capable of issuing a valid warrant under the provisions of the 2003 Extradition Act.
It was common ground that if she did not, there was no legal basis for extradition.
Ms Rose suggested it was obvious that a public prosecutor whose function it was to investigate and prosecute an individual "cannot exercise judicial authority in relation to that individual".
As a matter of fundamental legal principle dating back hundreds of years, a judicial authority had to be impartial and independent both of the executive and the parties in a case.
Clare Montgomery QC, for the Swedish Prosecution Authority, urged the judges - Lord Phillips, Lord Walker, Lady Hale, Lord Brown, Lord Mance, Lord Kerr and Lord Dyson - to reject the Assange appeal.
She argued that the High Court was plainly correct to accept that the term "judicial authority" had a wide and autonomous meaning, and it was not restricted in the way contended for by Ms Rose.
Since the start of the European Arrest Warrant (EAW) scheme it had been the practice of a number of prominent member states to issue EAWs through public prosecutors.
Ms Montgomery argued: "There is no conceivable breach of fundamental rights involved in such a process."
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