I'm not an expert in this area but from reading the Revenue website:
The nursing home must be on the Revenue's approved list of nursing homes
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Assuming that the home IS on the above list, you should be entitled to claim tax relief on the portion of Nursing Home fees which you pay which are NOT reimbursed by anyone, including your aunt
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Also, as far as I can see, the tax relief is at your high rate of tax and not the 20% rate, as with most (all?) other medical expenses.