extract from Part 3, section 31 of "Act for the Registration of Births and Deaths in Ireland"
20th April 1863 (histpop.org/irishstatuebook etc)
shall, at any Time within Twenty-one Days next after the Day of such Birth, give
Notice thereof to the Registrar of the District within which such Child shall have been
born;
The registrars had townland index books and up to date lists of electoral and dispensary districts
Interesting, but the revising 1880 Act omits the bit about "of the District" and just says "to the Registrar."
In any case, I have seen many registrations in the "wrong" district.