Two-year-old twins Maya and Karla Dickason and their older sister, Liane (6), were found dead in a Timaru house late Thursday evening.
Their mother, doctor Lauren Anne Dickason, has been charged with their murders.
The 40-year-old medical professional, who arrived in Timaru from South Africa - via MIQ - with her orthopaedic surgeon husband and their three daughters just over a week ago, was remanded in custody to a secure forensic mental health unit by Judge Dominic Dravitzki until her next appearance in the High Court at Timaru on October 5.
No plea was entered at the court appearance, her first since being charged.
The family's relatives were based overseas and they only had a small network of friends in New Zealand, Canterbury's police district commander, Superintendent John Price, said yesterday.
A family friend also told South Africa's netwerk24.com the family hadn't had time to make any new friends before Thursday night's tragedy.
"[The father] ... now he is all alone over there."
They were working with the girls' family through police liaison officers to help any urgent travel to New Zealand needed to provide support for family members in Timaru, MIQ associate deputy secretary Andrew Milne told the Herald.
"We are deeply sympathetic to the family here and overseas at this time."