I looked at the material. The 'corticioid' is Lopharia cinerascens, or at least the NZ version of that species (phylogenies indicate a complex). The fluffy thing is probably something else, but it is sterile so can't say much about that.
Peter de Lange
2017-01-17
2017-01-17
New Zealand, Waikato, Hamilton Basin, Hamilton Zoo
I am not sure if this is Phlyctis or another 'corticoid basidiomycete'. I think its a fungus rather than a 'lichen'. Seen occasionally on necrotic houhere (Hoheria populnea) branches on otherwise healthy trees. Exposed surface waxy, white. Inner surface of I assume the same fungus erupting through dead host tissue as white, pustular blobs of mycellium. Voucher: P.J. de Lange 13351 & T.J.P. de Lange, PDD