Final answer:
The prevalent eusporangiate fern during the Carboniferous period was Marattia, with Equisetopsida horsetails also forming large forests in swampy areas.
Step-by-step explanation:
The type of eusporangiate fern that was prevalent during the Carboniferous period is Marattia. During this period, the landscape was dominated by vast swamp forests comprised largely of ferns, horsetails, and club mosses. Specifically, Equisetopsida (horsetails) are mentioned as prolific during the Carboniferous, forming large trees and forested areas in swampy environments.
However, in the context of ferns, members of the Marattiaceae family, which Marattia belongs to, were also significant components of the Carboniferous flora. These eusporangiate ferns were characteristically large and formed part of the dense and diverse vegetation that contributed to the formation of extensive coal deposits from this era.