Fern Moss - Thuidium delicatulum

Thuidium delicatulum, often called Fern Moss.  

Thuidium really thrives in the shade but can tolerate some sun exposures once established

Fern moss looks like an assortment of tiny ferns. They have wide triangular leaves and the stem leaves are usually larger than the branch leaves. The leaves have very small thread-like branches on them and tiny bumps within the cell walls of the plant.