The cell is free, large, and irregular with a central inflated region from where branches extend in all directions. A test has never been observed. On the seabed, the presence of T. alba is indicated by a distinctive, slightly raised, approximately circular mound of 18–40 mm diameter through which there are many perforations. Reticulopodia are occasionally seen at the base of the perforations.
The test is free, irregular, monothalamous with a central
inflated region from which branches extend in all directions. The test is uneven, loose, very soft, flexible, and droops when picked above the water surface. The organism consists of a cell covered by a brownish proteinaceous organic lining to which foreign particles, detritus, small mineral particles or organic flecks adhere.