Quite numerous: Connacht, Belfast etc. See Conneely and Connolly.
Very numerous: Ulster, N Leinster, Connacht, but well-represented all areas. This name stands for at least two Irish names: Ó Conghaile, Connacht and Ulster; Ó Conghalaigh, Munster and Connacht. Woulfe mentions four septs: a family of the southern Uí Néill who were eventually settled in Monaghan: a group in Clare said to be descended from Mahon, brother of Brian Boru. Also there were two septs in Connacht. SGG.
Connolly: an-líonmhar ar fud na tíre: go sonrach i dtuaisceart Laighean, Ulaidh agus Connachta. Bhí clann amháin de chuid Uí Néill an Deiscirt lonnaithe in Oirghialla; ceann eile bhain siad le Uí Maine (Gaillimh). Féach Ó Coingheallaigh, leis.IF.
fairly rare: Galway etc. Ir.Lang. See Coneely and Connolly.