Tip Top is up for sale via Credit Suisse affiliate First NZ Capital, which is running a two-stage auction.
PEP's recent forays on this side of the Tasman have included Tegel Foods, as well as recently divested honey products business Manuka Health and its education portfolio company Academic Colleges Group.
Adamantem Capital bought New Zealand sausage maker Hellers last year.
The company also has Heritage Lifecare - one of the country's biggest providers of residential aged care and retirement services.
In Australia, Adamantem owns Hygain Holdings - a premium Australian horse feed producer, and specialised analytics consultancy, Servian.
Melbourne-based BGH Capital is a relative newcomer. The company, established in 2017 by Robin Bishop, Ben Gray and Simon Harle, is well-funded and has an Australian and New Zealand focus.
Fonterra announced the proposed divestment of Tip Top in December as part of an asset portfolio review and as the co-op seeks to reduce its debt.
While Tip Top was performing well, it had reached maturity as an investment for the co-operative, it said.
Tip Top has had several different owners over the years, after starting off as an ice-cream parlour in Wellington in 1936.
By 1962, its Mt Wellington plant had become the Southern Hemisphere's biggest ice-cream factory.
Two years later, Tip Top had expanded and a parent company - General Foods - was formed.
The company went to Goodman Fielder in 1987, Heinz in 1992, West Australia's Peters and Brownes in 1997, Kiwi Dairy Co in 2000, and to Fonterra in 2001.
