"What brings it to mind occasionally is when we have a visiting Australian Prime Minister or Cabinet minister who emphasises the special bond that Australia has with New Zealand.
"When, really, we don't have any bond at all in that respect [citizenship rights]. Actually, it is an anti-bond."
Treatment of New Zealanders who arrived in Australia after 2001 has been a growing point of contention between the two countries.
The changes in 2001 withdrew several types of benefit (unemployment, youth and sickness) for New Zealanders who enter Australia on a Special Category Visa.
The most significant change was to make it harder to get citizenship.
It required Kiwis to compete with other immigrants for permanent residence - which is capped - instead of being able to skip that and apply directly for citizenship.
The advert paid for by Mr Horton included a footnote outlining changes that were announced by Australian Prime Minister Malcolm Turnbull during a visit by Prime Minister John Key in February.
The change was that New Zealanders who arrived between February 26, 2001, and February 19, 2016, who have earned more than A$53,000 a year for five consecutive years will be able to apply for permanent residence and citizenship, from July 1, 2017.
At the time of the announcement, Mr Key estimated that up to 100,000 of the 305,000 Kiwis who arrived to live in Australia after 2001 could meet the criteria and get a new pathway to citizenship.
Mr Horton, who is married to Dame Rosie Horton and whose family were significant shareholders in former Herald owners and printing company Wilson & Horton, said that change did not go far enough and was limited to a certain time period.
He said last year the Australian declined to print his advert for reasons including factual accuracy. Fairfax did not respond to Mr Horton.
"That's fair enough, I don't have a problem with any paper not accepting an advert, that's their right."
