[4] A. mollis was first formally described in 1902 by the German zoologist August Brauer with its type locality given as the central Indian Ocean from a depth of 2,200 m (7,200 ft), collected on the Valdivia Expedition.

[3] Unlike most other deepsea anglerfish, H. mollis lacks pigmentation, and both sexes appear pallid and translucent, with the musculature and portions of the skeleton clearly showing through the skin.

Free-living males only grow to about 2 cm (0.8 in), and differ from the adult and juvenile females by the noticeable lack of a short, bubble-like esca and having comparatively small fins.

Further specimens have been found in the Pacific Ocean off eastern Australia, New Caledonia and New Zealand, with isolated findings near Hawaii and in the Gulf of Panama.

A papilla, or conical fleshy protuberance, grows at the site of attachment which may assist the male to establish a good grip.

The mouth of the male is partially blocked by the papilla, but an opening usually remains at either side which suffices for allowing a flow of water over the gills.