One customer in particular managed to download almost a terabyte of data, Telstra said.
Sydney resident John Szaszvari, a self-confessed "nerd", set out to outdo the 400 gigabytes of data he downloaded during a previous free data day.
Szaszvari told the Sydney Morning Herald he downloaded 14 seasons of MythBusters, 24 seasons of The Simpsons, the entire Wikipedia database, Microsoft software for his job, updates for his Xbox games and "a lot of random other stuff". He also synced all his Spotify playlists offline.
"Believe it or not I actually intend to watch it all - it's going to take a while but at least it's ready on demand," he said.
"It's always movie/TV night at my house at the moment."
He wrote on Reddit: "I'm the guy who downloaded 400+ GB last time. I must be the only Telstra user at home in my area or something because i'm still pulling 100+mbits. Been going since midnight and have just gone past my previous record."
Despite the massive amount of usage, Telstra is continuing to offer apologies to angry customers disappointed by slow download speeds and blocked usage during the free data period.
A strain on the network reportedly started to show by midmorning Sunday as customers took advantage of the opportunity to download and upload large files including videos, music and games for free.
Some customers used Reddit forums to report fast speeds up to 59MB per second in the early hours of morning but said they decreased to 35Mbps and then 4.8Mbps as the day wore on.
Others flooded Twitter with complaints.
"@Telstra free mobile data day turned into no mobile data day thanks to congestion.
Can't believe no one thought that might happen," one social media user wrote.
"I am hoping that a lot of people lodge complaints to the TIO for this farce that is a "free" data day," another posted on Twitter.
"Given the slow speeds being reported today, I'm wondering whether @Telstra's habit of offering free data punishes non-Torrenting users twice," one Twitter user wrote.
Tesla: Overall, the majority of customers continued to experience a reliable level of service and we look forward to continuing to provide this well into the future.
In a statement issued to news.com.au, a Telstra spokesman acknowledged there had been congestion to the network.
"We are also glad to see the underlying strength of the network demonstrated despite a few hot spots where heavy users caused localised congestion," the spokesman said.
"Overall, the majority of customers continued to experience a reliable level of service and we look forward to continuing to provide this well into the future.
"The previous record of 1,841 terabytes reached on our first Free Data Day was surpassed at 4pm AEST. We reached the peak network traffic level of the previous Free Data Day by 8am and stayed above that level until midnight.
"We're glad to see that our customers have been able to access free data all day on Sunday."
Earlier Sunday, a Telstra representative said the company was "seeing significant demand and have implemented software changes to stretch resources in the area to provide some relief".
A spokesman for Telstra said "there may be pockets of high demand in some areas during the day if a large number of customers are in a single area".
"This may cause periods of slower speeds however we don't expect this to be widespread and voice calls should not be affected".
The free data day is expected to cost the company millions of dollars, with Telstra anticipating customers to take full advantage of the offer.
The cause of the latest outage is still being investigated, according to Telstra.
It followed a major national disruption in February when an engineer accidentally switched off a core node.
The free data day was offered to every Telstra customer, including prepaid users with a zero dollar balance.
- news.com.au.
