"The public in New Zealand, from day one, have linked Red Nose Day with a New Zealand charity," he said.
"The Australian charity, contrary to what [lawyer for the Sids Council Clive Elliott QC] says ... over a number of exaggerated propositions, there's no reputation of his client in New Zealand other than what you would expect - a trace reputation among professionals."
Giving "a few brochures" to one organisation in New Zealand and claiming a 2 per cent internet traffic to its website from Kiwis did not amount to a significant presence in the country, Mr Miles said.
"The reputation is all ours."
The Sids Council would "never succeed" in registering the trademark in New Zealand because "the reputation is with my client", Mr Miles said.
"It's inevitable that there will be confusion arising out of the registration of their mark."
He added: "The courts have been prepared to say, where it's clear the primary reputation is with the proprietor of the trademark, who for whatever reason hasn't been using the mark for a while, the mark should stay, otherwise there would be confusion."
The Red Nose Day appeal "continues to have an extraordinarily high profile", which was only strengthened by the renewal of the appeal in recent years, Mr Miles said, slamming the Australian charity for trying to "muscle into the New Zealand market".
"They have no legitimate right to do so," he said, adding they had no donors and no sponsors in New Zealand.
Justice Simon Moore reserved his decision today.
Cure Kids chief executive Vicky Lee said they hoped to have his decision by Christmas.
"It's really up to the judge now, we have put our case forward to the judge and obviously they [the Sids Council] have. It will really be up to him now.
"It is quite frustrating and disappointing from our perspective having to do it because obviously we are just passionate about curing kids and continuing to fund that research."
When contacted, the Sids Council said they would not be making any comment at this stage.