Whether the latter outcome is just or desirable as a matter of law to be determined by the ACT Supreme Court, but for the merely curious, a termination of the inquiry at this point will leave some very interesting - and for Eastman, critical - questions hanging. If the DPP is successful, the ACT government will be under public pressure to have a wider inquiry, not one more narrow.

The DPP says the inquiry should be circumscribed, or quashed altogether, because the grounds upon which it was ordered in September last year by Justice Shane Marshall did not satisfy the legal requirements. An inquiry can consider only fresh information or argument, or matters which could not have been raised before the 1995 trial, the DPP says.

It's not a new argument, and has been rejected by the inquiry on several occasions; indeed, I understand that the ACT government will intervene in next week's hearing to oppose closure of the inquiry. The DPP could have appealed the Marshall decision last year, but did not. When it argued its propositions before the first judge to head the inquiry, Kevin Duggan, it was told it was too late - that the inquiry could not, as it were, rewrite the orders that conferred it with jurisdiction.

Later, the DPP, with fresh senior counsel on the case, argued essentially the same point to the new judge, Brian Martin, and got fairly short shrift for much the same reason. Only then did the DPP decide to do what he should probably have done in the first place, 15 months ago, if he wanted no inquiry: to appeal the decision by Justice Marshall in the courts. Since that time, the ACT government has spent at least $4 million on the inquiry (with the promise of about the same again if it is to be allowed to continue), and the DPP's own costs could hardly be less than $500,000 - including, probably, about $100,000 on arguing that the inquiry should not continue.

It's a rum old world in which the ACT government is paying for a judge and a substantial inquiry team, for a team of lawyers to agitate an issue on behalf of Eastman, for a team of lawyers (the DPP) arguing that the very idea of the inquiry is misconceived, for another team (the AFP) which cannot so far see what the fuss is all about, and, potentially, for a number of parties who may or may not be witnesses, but who have asked for the government to cover their legal costs.

One of those who is thought to have been given a grant for legal representation was an important scientific witness at the Eastman trial, Robert Barnes. The inquiry's terms of reference foreshadow a determined assault on his credibility and his findings in the case. Though Barnes has been in touch with the inquiry, it is understood that the inquiry has lost contact with him and would be delighted if he would renew it.

Another who has already appeared, by counsel, is the judge who conducted the trial, Ken Carruthers. The tribunal has become very interested in suggestions that the judge had access to a number of psychiatric reports, commissioned by police investigators, the existence of which was not disclosed until late in the trial. During the trial he also had conversations with a number of policemen who had been involved with the investigation, and who had been put on a security detail to protect him in case he was attacked by Eastman.

The tribunal is not examining

Carruthers' rulings or thinking processes. It is not determining whether he was, in fact, biased.

But it is interested whether his possession of the psychiatric materials, and meetings, however innocuous, with police witnesses could give rise to a suspicion in the mind of an ordinary observer about whether he could have been biased. That Eastman severely tested the judge during the trial, whether by hiring and sacking counsel, by insult, and by intermittent refusal to participate in the case, has also made relevant the judge's possession of psychiatric reports, because a live issue before the inquiry is whether Eastman was, at the time, mentally ill and legally unfit to plead.

Eastman's lawyers had been expressly forbidden to raise his fitness to plead before the judge. The prosecution team, inter alia in possession of reports by Dr Robert Milton, believe that Eastman was not mentally ill in the sense of being unfit to plead, and that, essentially, he was faking signs that he was in an effort to abort the trial. It did not raise fitness to plead, and, on at least one occasion, resisted an overture from defence lawyers, behind Eastman's back, that it do so.

Likewise, the judge at no stage raised the issue of his own motion, and, in sentencing, made it clear that he, like the DPP, believed Eastman's antics were contrived provocations. This was in line with the view of Dr Milton, although Dr Milton gave no evidence during the trial.

Oddly, when the fact of the existence of the Milton reports was raised late in the trial, the judge volunteered a remark that he knew nothing of them. But the then acting registrar of the court, Jill Circosta, has told the court that by then he had at least four or five. And she said she commissioned, at the judge's request, yet another. We do not yet know who first gave the judge any of the reports.

Likewise, when reference was made in court to a person there - in fact a detective on the judge's protective detail - the judge remarked that he did not know who he was. Defence counsel have already said this suggests the judge had some consciousness that these matters might raise issues about the appearance of bias.

Dr Milton has insisted that he was consulted by police about Eastman because police were worried that Eastman was dangerous, and a threat to the public. He has denied giving tactical advice to investigators, or being involved in any scheme to ''annoy'' Eastman, to ''drive him mad'' (as a senior AFP officer is said to have said) or to suggest tactics by which a rattled Eastman, after being provoked by overt and unfriendly surveillance, might suddenly confess all, perhaps to a designated father figure such as AFP Commander Ric Ninness.

Police witnesses called so far have themselves steadfastly and virtuously denied any harassment whatever of Eastman. Ninness and other lead investigators have yet to be called.

Interestingly, Dr Milton has affirmed that most of his judgments about Eastman are second-hand, depending primarily on what he was told by police. He has never spoken to him. He did, on several occasions, observe Eastman in court, and was shown transcripts of things Eastman was supposed to have said or done. Likewise, he read reports by other psychiatrists, including some who gave evidence during Eastman's attempt to get compensation over the way he was pushed out of the public service after an episode of mental illness in the 1970s. Milton came to disagree with some diagnoses, and, with the hindsight of further material from prison psychiatrists during Eastman's 18 years inside, is sure that Eastman is not, in the technical sense of the word, ''psychotic'' or ''paranoid''. He does, however have a paranoid personality disorder, he believes.

That opinion, or diagnosis, would prevail in his mind whether or not Eastman actually shot and killed Winchester. Milton's evidence, if accepted, might explain something of Eastman's thought processes, but do not of themselves offer evidence or insight into whether he did what he is accused of doing. Eastman has never made any admission - and even garbled recordings from his flat when Eastman was talking to himself can hardly be called confessional, except by those already convinced that he is guilty.

At one stage during the trial, when Eastman was being particularly difficult, the trial judge decided to put him in another room where he could see and hear the evidence but not have his interruptions annoy everyone. Doing so, Carruthers made reference to an article on the ''disruptive defendant'', written by another psychiatrist, to justify his decision. That article commented that in cases of disruption, the possibility of fitness to plead had to be considered, but, if the judge did consider it, he made no reference to any such consideration at the time, or in his sentence.

Had anyone, including the judge himself, formally raised the matter, the judge would have been obliged to halt the hearing, and to send to an expert mental health tribunal the question of whether Eastman was ''fit to plead''. A failure to do so, had it arisen during the Eastman appeal, would have been regarded by appeal courts as a fundamental defect in the trial, and would lead to orders quashing the verdict and causing a retrial.

But the question has been agitated as an issue only after Eastman's appeal rights were exhausted. A number of judges, included several High Court judges, have since then expressed concern about his fitness at the time of trial. But some courts and tribunals, and even this tribunal, have taken the view that a finding that there was an issue about Eastman's mental state is not a fundamental defect, but an invitation to decide how a mental health tribunal would have resolved the question, had it come before them.

Thus Chief Justice Jeffrey Miles, conducting an early narrow inquiry into Eastman's conviction, thought that a point was reached where the question of his fitness to plead had arisen. But he went on to find that in his opinion, Eastman was fit to plead.

The Miles inquiry, like this part of the present one, was focused on whether there was a doubt about Eastman's guilt. Such a doubt could arise from deficiencies in a trial, but an inquiry is not, of itself, an ordinary appeal or a review of the trial. It is, in effect, a reversed onus of proof investigation into a doubt about guilt: whether there are reasonable grounds for thinking that a convicted man might in fact be innocent.

There is no material ''proving'' Eastman's guilt that has been withheld from the courts. No extra material ''confirms'' the chain of circumstantial evidence initially put to a jury. The AFP is well aware of some of the deficiencies in the case put forward, or the investigation, but remains satisfied, uninclined to look for fresh leads, or information. Conscious decisions have been made at senior levels to do nothing that might suggest that police were taking a fresh look, or willing to be a part of any action that might lead to criticism of any of the investigators.

Although the inquiry has appointed a retired senior NSW detective to do some statement taking, and has commissioned expert evidence, it has not been able to mount an independent review of the evidence, or initiate any general inquiries.

That could have been among the powers of the inquiry, had it been directly commissioned by the ACT Attorney-General, Simon Corbell. But he consciously chose a more conservative inquiry, constrained by court-imposed terms of reference. The effect was probably to double the costs for about half of the breadth of inquiry possible.

If the Supreme Court is against him on Wednesday, he might have to have two for the price of three, anyway. Otherwise he may have to decide to leave the old doubts, and some new and refreshed ones, and Eastman hanging.