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fairly numerous: E Ulster. A Scottish name but also possibly a version of Hare, ie. O'Hare, q.v.
Quite numerous: E Ulster, Dublin etc. See Haire, O'Hare.
fairly numerous: Clare-Limerick etc. Ir. Ó h-Aichir, aichear, sharp, keen. A sept of Clare which originated with the Uí Fidhgheinte of Limerick. Mod. spell. Ó h-Eithir. Synonyms: O'Hare, Hare, Herr. IF & SGG.
rare: Limerick etc. Ó h-Eithir. A Limerick version of Hehir, q.v.
fairly rare: scattered. Ir. Ó h-Ír, Ó h-Éir from first name Ír (lasting). A sept of Oriel (Armagh). More usually O'Hare, q.v. MIF.
numerous: mainly Ulster and Connacht. Ir. Ó h-Ír. Ír was one of the mythical ancestors of the Gaels and a name meaning "long-lasting". A sept of Oriel (Armagh etc).MIF.
Quite numerous: Munster etc. Ir. Ó h-Eithir, more correctly Ó h-Aichir, aichear, sharp of speech. A sept of Clare, originating in Limerick. See also Hehir & Herr. IF.