The Federal Court is expected to hear closing arguments today and there is a small chance the verdict will be announced later today, although a decision is more likely to happen after Easter.
The case opened yesterday with Australia Post arguing that its rival's name was too similar.
However, Digital Post Australia said it would "defend vigorously its right to a name that reflects accurately what the business does".
Rivals Salmat and Computershare stole a march on Australia Post when they announced Digital Post Australia (DPA) on 15 March. The service will provide a free "digital postbox" for every Australian household.
The companies each hold a 40% stake with the final 20% held by US firm Zumbox, which developed the software platform behind DPA.
Australia Post announced its own Digital MailBox service in a statement on 26 March.
"The Australia Post Digital MailBox will allow businesses, government entities and customers to communicate through a secure online portal that can be accessed 24 hours a day, seven days a week, wherever they are," said Australia Post chairman David Mortimer.
"Just as the traditional letterbox has been a vital part of people's communications for the past 200 years, we think a personal digital mailbox for every Australian is the perfect complement to the letterbox in this online revolution."
However, the postal agency made no mention of the technology platform it planned to use, a fact that didn’t go unnoticed by DPA.
According to DPA: "Following Digital Post Australia’s announcement [on 15 March], Australia Post then followed up two weeks later with a similar statement. Its announcement contained no detail about how it intends to execute its own plan.
"Most critically, there was no mention of the technology it will use to make it work."
DPA chairman David Hynes said his company was entitled to use its name.
"Our name says what we do – which is providing digital postal services to the people of Australia," he said.
"We were the first in this market to launch digital post and we are best placed to provide this service, efficiently, securely and for free…
"We have been working on this and talking to the mailers and aggregators for more than a year. It is interesting that faced with competition, Australia Post have chosen to take the legal path."
An Australia Post spokesperson told ProPrint he would respond in due course.
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