In addition to the family descended from the Hayde family described in the New Zealand, India and England families (Tree # 1), there is another Hayde family in Auckland.
This family is descended from a James Hayde born in Dublin around 1800.
James was a wool dyer. He and (probably) his brother Patrick Hayde (a spinner) both lived in the Tenters/Newmarket area of Dublin in the 1820s.
They both had children who all lived in and around Dublin City, just south of the river. Some were painters in the 1850s, some were newsvendors and several joined the army.
Some descendants still live in Dublin while some have moved to London and one emigrated to Auckland in the 1950s. A copy of this tree is at https://www.ancestry.co.uk/family-tree/tree/52117927/family
A member of this tree has done a DNA test and the results are very similar to those for descendants of Tree #1 and others that originated in Tipperary. Thus the James and Patrick who were in Dublin in 1820s have Tipperary roots, but the connection is unknown.