Kingdom: Fungi
Phylum: Basidiomycota
Class: Basidiomycetes
Order: Agaricales
Family: Marasmiaceae
Genus: Marasmiellus
Species: M. candidus
Binomial name: Marasmiellus candidus
Synonym: Marasmius candidus, Agaricus candidus, Epicrisis Systematis,
Marasmius magnisporus, Marasmiellus albocorticis, Marasmiellus albus-corticis.

Marasmiellus candidus in one of about four fungi in the genus Marasmiellus recorded in New Zealand. Marasmiellus species are small, tough mushrooms on fallen wood, twigs and leaves.

http://virtualmycota.landcareresearch.co.nz/webforms/vM_Species_Details.aspx?pk=34870

The photographs below are small fungi found growing in June of the end of a cut log in a damp shaded area by Kendall place entrance to the Te Henui Walkway.
White fungi Genus Marasmiellus.JPG

White fungi Genus Marasmiellus-001.JPG

Thanks to Wikipedia for text and information: https://creativecommons.org/licenses/by-sa/3.0/