By tradition members of the sovereign's family received titles associated with England, Scotland and Ireland, the three kingdoms that made up the United Kingdom. The dukedom of Connaught was named after one of Ireland\'s four provinces, now known by its modern Irish language-based spelling of Connacht. It was seen as the title that if available would henceforth be awarded to a monarch's third son; the first son was traditionally Duke of Cornwall (in England) and Duke of Rothesay (in Scotland), and would be made Prince of Wales at some point, while the second son would often become Duke of York, if the title was available.
Since the exit of twenty-six counties of Ireland (in the form of the Irish Free State, now called the Republic of Ireland) from the United Kingdom in 1922, titles related to locations in the twenty-six counties have not been awarded (though Prince Edward, Prince of Wales - later King Edward VIII (r:1936) - was made a Knight of the Order of St Patrick, an Irish Order of Chivalry which has since lapsed.) However territorial titles relating to Northern Ireland have continued to be awarded.
It was speculated that in view of the warming of relations between the United Kingdom and the Republic of Ireland in the 1990s Queen Elizabeth II might award her son, Prince Edward the dukedom of Connaught. This did not happen however.
After Prince Arthur's death in 1942, the title was inherited by his grandson, Alistair. In the absence of any male heirs, the dukedom became extinct with Alistair's death, which occured only four months after his father's.