Graham Dwyer has told the Court of Appeal he did not send a text message to Elaine O'Hara saying he would like to stab a girl to death.

Dwyer made his intervention from his seat in court on the second day of his appeal against his conviction for the murder in 2012 of Ms O'Hara.

It was the first of three interjections from Dwyer during submissions by prosecuting counsel, Sean Guerin. After the third interjection, Appeal Court President Mr Justice George Birmingham said he would have Dwyer removed to the cells if there were any more.

Dwyer is appealing his conviction on a number of grounds. A significant part of his appeal focuses on the retention and accessing of data relating to his work mobile phone, which his lawyers say was used to link him to other phones and to messages sent to Ms O’Hara.

The legislation allowing this data to be stored and retrieved was found to breach EU law, and Dwyer’s lawyers say he wants a retrial where the admissibility of this evidence could be tested.

Dwyer denies being the person who bought and used a phone later found in Vartry Reservoir in Wicklow, to send the message about stabbing and other messages to Ms O'Hara culminating in a text to "go down to the shore and wait" on 22 August 2012, the day she was last seen.

Mr Guerin began the prosecution submissions to the appeal court by setting out the extent of the evidence against Dwyer at his trial, even without the disputed mobile phone data.

He began by reading a text message sent to Ms O’Hara in June 2011 from the phone number which the prosecution says was used by Dwyer. The person writes that he wants to stab a girl to death some time.

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Mr Guerin said the prosecution case is that the text was sent by Graham Dwyer, that he meant what he said, and that he did what he said he was going to do. Mr Dwyer, who is sitting in the seating area reserved for accused people and prisoners at the side of the court, interjected to say, "I didn’t say any of that".

Mr Guerin said that in the trial, the prosecution had to prove Dwyer was the author of the texts, that the desires expressed in them were real and reflected the formation of a longstanding intention to kill.

He said the prosecution also had to show that the circumstances of Elaine O’Hara’s disappearance and death could only be explained by the realisation of that intention and to eliminate the possibility of suicide.

Mr Guerin said the author of the text messages told Elaine O’Hara he was going to take her to woods, tie her up and stab her. Ms O’Hara replied that she was not going to commit suicide. Mr Guerin asked if Ms O’Hara had taken her own life, how did her keys, phone and some of her clothing get to the lake at Vartry Reservoir from the mountainside where her body was found.

Mr Guerin said there was an utterly overwhelming case to prove Dwyer was the author of the texts to Elaine O’Hara even without the call data records disputed by Dwyer.He said Dwyer was significantly overstating the value of the call data.

Gardaí had employed old-fashioned detective work to read text messages, there were printouts of Dwyer’s bills from his workplace, showing extensive contact in earlier years between him and Ms O’Hara, and there were texts on Ms O’Hara’s phone and backed-up on her laptop.

As Mr Guerin went through what he said was the evidence that Graham Dwyer was the person using a particular phone to communicate with Ms O’Hara, Dwyer interjected twice more from the dock.

Mr Justice Birmingham told his defence counsel, Remy Farrell, the court had ignored the previous interruption but he said if there was another one Dwyer would be removed to the cells.

Dwyer told his solicitor he couldn’t "listen to this", but there have been no further interruptions.

Taking the court through some of the text messages produced in evidence during Dwyer’s trial, Mr Guerin said it was utterly implausible that there was another person in the world who had a child born on the same day as Dwyer’s child with the same name, who bought a bike on the same day, who got a pay cut on the same day as Dwyer, who came 5th in a flying competition on the same day and was at a reception for the Polish ambassador on the same day as Dwyer.

Prosecuting counsel, Annmarie Lawlor, told the court explicit videos of Dwyer had been shown to the court during the trial because they wanted the jurors to be able to compare and contrast the videos with the content of Graham Dwyer's interviews with gardaí where he feigned disgust at the content of text messages.

And she said they were shown in response to the defence claim that documents found on Dwyer's devices, as well as text messages discussing killing and raping women, were so outlandish and outrageous that they had to be just a fantasy.

Ms Lawlor said a complaint about the judge’s demeanour in court was "nebulous" and was not a matter that could have led to an unfair trial.

She also told the court the trial judge was absolutely correct to refuse to direct the jury to find Dwyer not guilty because of a claimed lack of evidence about Ms O’Hara’s cause of death.

The jury had material before them to allow them to weigh up and evaluate if she took her own life. And she said it was open to the jurors to infer from the evidence that when Dwyer said he would do things, he meant it. She said the evidence showed he did exactly what he intended to do.

The three judges said they would give their decision as soon as they could but given the length of the case and the detailed submissions they had received, it should not be expected imminently.