Liverwort species may be either dioicous or monoicous. In dioicous liverworts, female and male sex organs are borne on different and separate gametophyte plants. In monoicous liverworts, the two kinds of reproductive structures are borne on different branches of the same plant.ome of the more familiar species grow as a flattened leafless thallus, but most species are leafy with a form very much like a flattened moss. Leafy species can be distinguished from the apparently similar mosses on the basis of a number of features, including their single-celled rhizoids.