The process in which the anatomical structure of the adult male tail tip is generated and organized. In some species of rhabitid nematodes, the male tail tip undergoes a morphological change such that the most posterior hypodermal cells in the tail (
hyp8-11 in C. elegans) fuse and retract anteriorly, changing the shape of the tail from a pointed, tapered cone, or spike, to a rounded, blunt dome.