For primary school aged pupils, six out of 10 students said that was the case in their households.
A total of 16 per cent of high schoolers said there was a limit on screen time at home, while 37 per cent of primary school students reported having a limit.
Those pupils who had limits said they were allowed an average of an hour on the computer or other digital device. High school students had an average of two hours allowed to them.
CensusAtSchool co-director Rachel Cunliffe, a mother of four children aged under 8, said she was very surprised by the results.
"I imagined that in this completely wired world, the majority of kids would have limits. Parents often discuss ways to find a balance between screen time and outdoor play time.''
Within her own family, she and her husband tried to set limits but with four young children, that was often hard to police.
"Now, in our house, we have a list of morning, afternoon and evening jobs to be done on school days before the kids are allowed screen time,'' she said.
"By the time they've done everything expected of them and their out-of-school activities, like swimming and karate, they're not often long periods of time left for gaming.
"My 8-year-old has been pretty motivated to get through his jobs and can get in an hour on the Playstation or tablet sometimes.''
The study also revealed what students said they did most when using a digital device.
Four in 10 students said they enjoyed gaming activities. Most of those were teenage boys, with a median of two hours in front of an Xbox, Nintendo, Playstation or similar console.
Thirty-two per cent of primary school aged girls said they used a cell phone to send texts or instant messages.
Teenage boys and girls said they spent most of the time on social media when they were on their cell phone, with 49 per cent of girls and 31 per cent of boys doing so.
Internet safety group Netsafe stressed the importance of parents maintaining supervision and an active role in helping their children to have a positive online experience.
Chief executive Martin Cocker said although children nowadays were quick to understand how to use digital devices, they were sometimes not emotionally or mentally prepared for other issues such as online abuse or cyberbullying.
"We need to teach and model appropriate online behaviours, how to keep safe and where to get help if it's needed," Cocker said.
"That means knowing what your kids are doing online."
