He met up with the girl a day after their first encounter, and she brought her mother. Davie asked to meet her again without her mother present.
Police intercepted him at the third meeting, and it was then they discovered a collection of text messages showing his plans to pay for sex with another child.
The 10-year-old victim's grandmother cannot be named, to protect the identity of the child, who does not know about the offending.
The woman, who is a prostitute and knew Davie as a client, began arranging in May 2017 to bring the girl to him so he could touch her and possibly have sex with her.
The grandmother sent Davie photos she had taken some time earlier of the victim naked in the bath.
If somebody had said 'I've been with a 4-year-old', I'd say 'I've been with a 3-year-old.
Davie paid for a phone top-up for the woman so she would send him the pictures.
The Crown said the abuse never got a chance to play out because Davie was caught grooming the teenager, but Davie claims he never intended to go through with the plan, and that he was just "talking rubbish" to take his mind off his other problems.
He said he knew the grandmother would never follow through either as she was always putting off arrangements to meet.
During cross-examination in Friday's hearing, he said he had no sexual interest in children, despite sending graphic texts describing the sexual things he wanted to do to kids aged 8-16.
He said if someone said something to him in a conversation he would always say something worse so the fantasy would escalate.
"If somebody had said 'I've been with a 4-year-old', I'd say 'I've been with a 3-year-old," he said.
But detailed texts between the pair show them discussing payment for the girl, with Davie first offering $1000, and the grandmother then saying she wanted a cheap, reliable car as payment.
They discuss how Davie can gain the girl's trust, whether she needs to take time off school, and that they should go shopping to buy her a bra and underwear set so Davie would have an excuse to see her in it.
He had earlier spoken about a transgender person, Morgana Platt, from Palmerston North, who had planned to train a child for sexual exploitation.
His text messages show he sent the nude photos of the girl to Platt and discussed having Platt come over when the girl and her grandmother were there.
A search of Davie's computer revealed a bestiality video and a written story about incest with children.
The grandmother was found to be in possession of bestiality images as well.
Her defence lawyer said her role as an escort involved engaging in sexual fantasies when corresponding with clients, and that her text messages to other people showed her entertaining such fantasies without the intention of following through.
She possessed the bestiality images to use with other clients, he said.
Friday's disputed facts hearing was for Judge Jan Kelly to decide whether it was an aggravating feature of the offending that the pair would have gone through with it, or whether it was not an aggravating feature because as the defence said, it was only ever a fantasy.
She has reserved her decision.
News of the offending follows the sentencing of Auckland woman Kasmeer Lata, who forced her daughter into prostitution in what is only the third slave dealing case in New Zealand.
Lata received a six-years-and-11-months prison term, while her partner and co-offender Avneensh Sehgal was sentenced to four years and eight months in jail.
The shocking case was used as a case law example in Friday's discussions.
