The businesswoman and sometime escort went missing on November 19, hours before her baby daughter was found abandoned in her pram in a street at Manly on Sydney's northern beaches.
The court has been told police trailed Wallace to a remote bush location 35km east of Lithgow in March 2004, after he told an undercover police officer he was going to dig up Ms Zou's remains.
Her skull, jawbone and other skeletal pieces were found in a garbage bag in the back of his ute.
Wallace admits shooting Ms Zou and taking steps to cover up his involvement, including lying to police, fabricating alibis and burning out her Peugeot, but says he was provoked.
The jury has been told Wallace spent time in jail and lived an itinerant existence, without any fixed address. He was unemployed and supported himself by
Despite having an ongoing sexual relationship with Ms Zou and lending her $5000 to help with her import business, Wallace did not come forward in the days after her disappearance, until his photograph was circulated in the media.
Images of him and Ms Zou, taken from CCTV footage of her apartment block, were released by police in a public plea for information.
Wallace told police he was wary of coming forward.
"I have not always had a happy relationship with the police and I don't need this," he said in a November 2003 police interview played to the court today.
"I am trying to get on with my life, I'm trying to rebuild, I don't want any drama."
"If I come forward and speak to you, you are not going to believe me, there's going to be a shit fight."
In the months before her murder, Wallace said, Ms Zou had a falling out with her lover Tim Titheradge, the father of her child.
"She said, because Tim, in her sort of terms, was not 'playing the game', she'd decided to remove him (as her next of kin)," Wallace said.
Wallace told police he had received a head injury while he was in jail, and had some brain damage.
"It's not that I'm trying to be deliberately evasive, but I lose the thread of things sometimes, you know, concentration-wise," he said.
"It's part of this problem with the brain ... I just get tired and I can't focus."
The trial, before Justice Bruce James, is continuing.
