25 Companies not resident in the State
(1) A company not resident in the State shall not be within the charge to corporation tax unless it carries on a trade in the State through a branch or agency, but if it does so it shall, subject to any exceptions provided for by the Corporation Tax Acts, be chargeable to corporation tax on all its chargeable profits wherever arising.
(2) For the purposes of corporation tax, the chargeable profits of a company not resident in the State but carrying on a trade in the State through a branch or agency shall be-
(a) any trading income arising directly or indirectly through or from the branch or agency, and any income from property or rights used by, or held by or for, the branch or agency, but this paragraph shall not include distributions received from companies resident in the State, and
(b) such chargeable gains as but for the Corporation Tax Acts would be chargeable to capital gains tax in the case of a company not resident in the State;
but such chargeable profits shall not include chargeable gains accruing to the company on the disposal of assets which, at or before the time when the chargeable gains accrued, were not used in or for the purposes of the trade and were not used or held or acquired for the purposes of the branch or agency.
(3) Subject to section 729, where a company not resident in the State receives any payment on which it bears income tax by deduction, and that payment forms part of, or is to be taken into account in computing, the company’s income chargeable to corporation tax, the income tax on that payment shall be set off against any corporation tax assessable on that income by an assessment made for the accounting period in which the payment is to be taken into account for corporation tax, and accordingly in respect of that payment the company shall not be entitled to a repayment of income tax before the assessment for that accounting period is finally determined and it appears that a repayment is due.
Member States cannot apply a higher tax rate to profits of a branch than a resident company. Royal Bank of Scotland plc v Greece (C-311/97)  STC 733.
Irish branch investment funds not under its control are not taxable. S Murphy (Inspector of Taxes) v Data Products.  ITR Vol 4 page 12. CLTP 21.8.
Corresponding UK Tax Provision
Section 11, Income and Corporation Taxes Act 1988. Now re-enacted at various places in the Corporation Tax Act 2009. Refer to the Destination Table of that Act for details.
Sections referred to in text
section 729 [Income tax, foreign tax and tax credit]
247 Relief to companies on loans applied in acquiring interest in other companies
590 Attribution to participators of chargeable gains accruing to non-resident company
729 Income tax, foreign tax and tax credit
745 Charge to income tax or corporation tax of offshore income gain
864 Making of claims, etc
884 Returns of profits