Dublin's half-barony came under the County Council of Dublin, as Rathdown (No.1 District). Rathdown (No. 2 District) was under Co. Wicklow. Dún Laoghaire (or Kingstown as it was known 1821-1920) was originally a fishing village called Dunlary or Dunleary, and as such was in the Dublin half-barony, but after the new town was built it had a separate local Government as a borough council from 1821 up to 1994.
The old Rathdown half-barony does not correspond exactly with the new county area, as it included Rathfarnham and Terenure (See Map here), but when the new county was set up in 1994 the name had resonance of past connections