The man accused of murdering a jogger in an upmarket Auckland suburb can be revealed as Tevita Mafi Filo.

Joanne Marie Pert, 41, a student and mother of two, lived in central Auckland and was on a regular run through Remuera when she was allegedly attacked on Shore Rd on January 7.

Filo, from Mt Roskill, turned up at Auckland Central Station on the same day.

The 24-year-old appeared in the High Court at Auckland this morning where his lawyer Louise Freyer accepted name suppression should lapse. However, there are several other orders restricting publication.

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No pleas were entered today.

Filo appeared in the dock with a support person.

He is understood to be from a large Tongan family, but there was no sign of relatives or friends in the public gallery.

He wore a white T-shirt and had plasters on his left arm, and stared intently at Justice Simon Moore throughout the appearance.

Filo's facial hair was overgrown and he was of short stature and slight build.

The sister of Filo wrote a message to her brother a day after he turned up at the police station.

Filo's younger sister, who the Herald has decided not to name, posted a photo of herself and older brother "Vita" on Facebook on January 8.

Ms Pert was killed the day before.

Filo's sibling accompanied the photo with a message to him: "I love you my brother. Your baby sis is here praying for you. I love you."

In another message, she told friends and family that life was a struggle, "especially when your family ain't complete with one more person missing".

Ms Pert collapsed on the front lawn of a Remuera house, just metres from the front door. Some time later, the occupants saw her from their window and called for help.

Emergency services were called just before 11am but Ms Pert was dead when they arrived.

It is understood when Filo handed himself in at Auckland Central police station he carried with him a weapon which police believe he used to kill the woman, but the nature of the weapon and the injuries sustained by the victim have been suppressed.

Ms Pert's ex-partner is rich-lister Culum Manson. Manson, 40, is a director of family business Mansons TCLM - one of New Zealand's biggest construction firms.

Last year's NBR Rich List estimated the family's wealth at $450 million and last year the company announced it was working on three big new Auckland office blocks, worth about $220 million.

Filo will be back in court in April. A four-week trial was set down for November.