Liverworts are primitive nonvascular plants, perhaps the most primitive true plants still in existence. There are two types. In thallose liverworts, the plant body (thallus) consists of flattened masses of cells that look leafy but show little differentiation into different cell types.oth types of liverworts are small, in the range of a few millimeters to a few centimeters, and easily overlooked. Some species, however, are conspicuous members of the forest-floor flora and may be much easier to find. One of these is Marchantia polymorpha. a thallose species.