But the group interviewed for the study were younger, with an average age of 24, and none was in full-time work.
Onehunga builder Daniel Phillips, 28, had to stop work when he took in baby son TK two months after he was born last year.
"I was not happy with the care he was getting from his mum," he said.
But when he took TK into his own care and applied for the domestic purposes benefit, Work and Income made him "jump through hoops".
"I had to get his mother to write a letter to prove to them that I was going to be a solo dad," he said.
Like many solo dads in the study - and many mothers at home with young children - he felt isolated at first.
So he started taking TK out for a daily walk around nearby One Tree Hill.
"To get out and see other people made me feel heaps better."
But his reception, from mothers who were also out in the park with their children, was mixed.
"Since I've been a solo dad I've met a lot more solo dads and we've all come to the conclusion that we're looked down on. It's not very nice, that we're not 'real men'. Whereas I look at it through my eyes - it takes more of a man to stand up for his children than it does for a man to just go to work and put his baby in care."
Mr Phillips, who is now doing a civil engineering degree as well as caring for TK, has found "awesome" support from agencies including Plunket, Barnardos and the Father and Child Trust.
But study author Harald Breiding-Buss said some agencies, such as Parents As First Teachers, did not even have enrolment forms suitable for solo dads. Their form asked for "mother's name" and "partner's name", he said.
"The advice we give to all professionals is that when they work with families they should create an expectation that their service is for both parents."
The Father and Child Trust has a "Fathers' Day jamboree" with barbecue and bouncy castle for all dads and kids at the Onehunga Community Centre from noon until 4pm on Sunday.
GOING SOLO
Number
* Solo dads: 24,036
* Solo mums: 120,996
Aged under 30
* Solo dads: 11.5 per cent
* 23.8 per cent
Aged 30-39
* Solo dads: 29.1 per cent
* Solo mums: 35.6 per cent
Aged 40-49
* Solo dads: 40.2 per cent
* Solo mums: 32.5 per cent
Aged 50-plus
* Solo dads: 19.3 per cent
* Solo mums: 8.2 per cent
Employed full-time
* Solo dads: 59.3 per cent
* Solo mums: 31.0 per cent
Employed part-time
* Solo dads: 8.0 per cent
* Solo mums: 20.6 per cent
Unemployed
* Solo dads: 6.5 per cent
* Solo mums: 8.3 per cent
Not seeking paid work
* Solo dads: 26.1 per cent
* Solo mums: 40.1 per cent
Source: Statistics NZ
ON THE WEB
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