
Thyrsopteris elegans is the only living species of the Thyrsopteridaceae, a family of tree ferns that was diverse and widespread during the Mesozoic. Cretaceous fossils are known from mainland Chile, but nowadays Thyrsopteris is endemic to the Juan Fernández Islands...
Pellaea rotundifolia is endemic to New Zealand. It is a popular house plant worldwide and was observed growing outdoors in California.
Nice! Looks like P. cernua to me.
Thanks!