Where does a non-resident with no Irish income pay tax?

My query is on someone who spends the year travelling, has been non-ordinarily resident in Ireland for 2 years, spends so little time in any country he is not resident anywhere.
I understand he is liable for tax on any Irish source income, and all remitted income, but what about non-Irish, non-remitted income? Should he be registered for tax in every country in which he provides his services??

A non resident and non ordinarily resident individual will be liable to Irish income tax on Irish source income only (remittance basis doesn't apply). My understanding is that the tax rules in each country in which he is present would have to be looked at to determine the tax position in that country. Many countries will tax a non resident on a similar basis to Ireland i.e. only on income arising in that country. The only way around registering and filing in each individual country is if he was tax resident in a country and could avail of Double Taxation Agreements with those other countries to exempt his income from tax.