Thread by @jlpobrien

Counties/states with the largest Irish-born populations in 1871:
New York (528,806)
Cork (501,664)
Antrim (391,816)
Dublin (378,451)
Galway (246,275)
Mayo (244,108)
Down (288,673)
Pennsylvania (235,798)
Donegal (216,619
Massachusetts (216,120)
Tipperary (213,165)

Tyrone (210,181)
Lancashire (200,061)
Kerry (195,085)
Limerick (189,153)
Armagh (177,085)
Derry (171,311)
Ontario (153,000)
Clare (146,918)
Cavan (140,029)
Roscommon (139,625)
Wexford (131,286)
Waterford (121,040)
Illinois (120,162)
Sligo (114,484)

Monaghan (114,212)
Kilkenny (108,232)
Lanarkshire (104,656)
Victoria (100,468)
Leitrim (95,206)
Meath (94,628)
Fermanagh (91,867)

The 32 counties (and states)! Sources are Censuses of Canada, England & Wales, and Ireland of 1871.

New Jersey (86,784) just missed out ...

Irish-born population in 1870/71:

Ireland (5.2m)
USA (1.9m)
England & Wales (570k)
Canada (220k)
Australia (210k)
Scotland (210k)
New Zealand (30k)
South Africa (4k)

Nearly 40% of people born in Ireland were living outside of Ireland

(The US Census 1840 did not ask about birthplace, so not possible to compare pre-Famine. Also there's sometimes a lack of data for people born in Northern Ireland living in other countries (grouped with UK-born). Not sure data available for long-term comparisons, unfortunately.)