Continuation (at this Co. Leitrim Queries website) of a list of Irish surnames and the counties/baronies where they are most predominant.

1. Hallahan: Cork
2. Hallissy: West Cork and South Kerry.
3. Hanafin: Kerry.
4. Hanna: Antrim and North Down.
5. O'Hare: East Armagh and West Down.
6. Hargadon (Hardiman): Galway.
7. Hassett: Clare and North Tipperary.
8. Heanue: West Galway.
9. Henehan: Mayo.
10. Hennelly: Mayo.
11. Henrion: Westmeath.
12. Hession: North and East Galway and South Mayo.
13. Hever: Sligo.
14. Histon: Limerick.
15. Hoban: Mayo.
16. Holian: South Galway.
17. Honan: Clare.
18. Hood: West Antrim and East Derry.
19. Horaho (alias Harrison): Sligo.
20. Horgan: Cork and South Kerry.
21. Hosty: Mayo and North Galway.
22. Hourihane: Cork.
23. Hoyne: Kilkenny.
24. MacHugo: Galway.
25. Hultaghan: Fermanagh.
26. Keady: South-West Galway.
27. Kearon: Wicklow.
28. Keaveney: North-East Galway.
29. MacKeever: Derry and West Antrim.
30. Keohane: Cork.
31. Kernaghan: Armagh.
32. Kerwick: Kilkenny.
33. Kett: West Clare.
34. Kevane: Kerry.
35. Keville: Galway.

More to follow - this is a general guide for research, and there are exceptions, of course.