He had pleaded guilty to that charge and another of possessing on his mobile phone a text document entitled Daddy's Baby Girl, a story about a sexual relationship between a 7-year-old girl and her father.
He was sentenced to six weeks in prison for that offence, to be served concurrently.
Outside the court, Ms Samson said she was "absolutely shocked'' by the leniency of the sentence.
Crown counsel Robin Bates told the court the Crown could not prove who had caused the broken bones, as the house in which the family lived had several occupants, most of whom had "a history of violence''.
The prosecution had proceeded on the victim's brain injury, as Nuku's involvement in that could be proved.
The victim's mother had witnessed the end of the incident.
Nuku's counsel, John Westgate, said his client accepted "full and complete responsibility'' for the victim's head injury, but nothing else.
It had been "a particularly stressful time'' for Nuku, who had recently started work.
According to the summary of facts, Nuku spent much of his time playing games on his Xbox.
He was "often unco-operative'' when asked by the victim's mother to help care for the children.
The mother was having a shower when the victim's crying interrupted his game, "resulting in him becoming angry''.
"The defendant held the victim by the arms and shook her violently.''
The baby suffered bleeding in the brain, on the surface of the brain, in the middle membrane and in both retinas.
She was taken to Dunedin Hospital on April 10.
Ms Samson, gave a tearful victim impact statement.
"Everything changed when she was assaulted by you,'' she told Nuku, who stood impassively in the dock.
Her daughter would not grow up like normal people, but would be permanently affected.
She would also grow up knowing it was her father who had caused her injuries.
"You have broken her in every possible way.''
Ms Samson said she had not been able to see her daughter for 12 months and had limited supervised access with another daughter.
Her own family no longer trusted her and she would suffer guilt for the rest of her life.
Judge Michael Crosbie told Nuku he was aware some in the community would "throw the book at you'' if they had the chance, but he had to be even-handed and take note of other court rulings.
Some would ask why more serious charges had not been laid, but he said charges resulted in an assessment of a variety of guidelines, including the availability of evidence.
An issue for him was whether or not Nuku had faced up to what he had done. Nuku had determined the victim's life would be one of suffering, and dependence on others.
A probation report said Nuku had failed to take responsibility for what he had done.
A report from a pediatrician said seizures the victim had developed were hard to control, and would likely continue for the foreseeable future.
Now 16 months old, the victim had the development of a 4-month-old, could not walk or even crawl, and could only roll from her back on to her stomach.
Outside the court, Ms Samson said the victim impact statement could not get across the depth of the hurt that had been caused by Nuku.
She was "absolutely shocked'' at the sentence, which was "definitely'' not enough.
"It will never be enough.''
