Thanks for the reply
I think the same problems occured in Scotland before 1879 when compulsory education was introduced, and names took on some weird and wonderful spellings. So far for Ann Malarky I also have Milarkey and Millarky, but the favourite now seems to be McLarky. This might be the Scottish connection with Mc and Mac as clan names, but it has turned up for Ann and this has lead me to her parents. Her father is also listed as McLarky (Denis) although still no location in Scotland or Ireland for either of them being born. Her mother was Elizabeth Anderson which does not lead me much further because I would imagine that this is a common surname both sides of the Irish Sea. Most of Ann's certificates relate to either central Glasgow or to the 'Celtic end' of the city, and her marriages were to a Patrick Gallacher and to a John McCready (both weddings in Glasgow) which both have Irish catholic sounds to them (this is a guess from an east coast protestant point and could be completely wrong). My local research expert thought that the Millarky family may have been part of the Irish travelling people, and this would fit because her first husband was a cattle drover. He suggested Sligo and Mayo might be a good place to start looking but so far no luck. He also thought of a catholic background because of the number of Millarky's who were involved in voluntary or forced expatriation to Australia in the 1800's. I haven't found any census data in Scotland so far but I have family in Glasgow and will try to get some time in their local library to look up what they have in the future.
Hope your own links turn up soon