Would an alternative translation of 'the parsnips belong to Owen' also be acceptable?
Eiddo is used mostly for "property" today, so Eiddo Owen yw'r pannas is better translated "The parsnips are Owen's property".
I'd say Mae'r pannas yn perthyn i Owen for "The parsnips belong to Owen".
It's a lovely word. Perthyn i, as well as meaning "belong to", can be translated "be related to". So Dw i'n perthyn i Siân means "I'm related to Siân" - literally "I belong to Siân".
It's also a very Welsh idiom - very often you would hear Welsh people (particularly my grandparents generation) saying in English - "She's belonging to the family from up the road" or something like that :-)