"Have now been advised that ex-spouse may try to lay claim to a portion of my home! Is this a possibility?"
Yes, it is a possibility. This does not arise from your spouse having some particular entitlement to a portion your home. However, there is no such thing as a "clean break" divorce or separation in Ireland. Either spouse can always go back into court to seek a property adjustment. In this case, if your ex spouse owns no house, and if a court feels you are in a much better financial position than your spouse (and if there are no circumstances which would make a court disinclined to help your spouse), it is entirely possible that your spouse could succeed in a claim for something. If your spouse is in fact much worse off than you, and if you accept that your spouse's previous relinquishment of rights is what got you on the property ladder (while your spouse was left behind - if that is the case) then I think that if you examine the situation objectively, you might even agree that your spouse could be morally entitled to something.
Of course, no single facet of a separation\divorce case is looked at in isolation. The courts would be slower to make an adjustment in favour of an alcoholic\gambler\person who abandoned small children etc., etc. so I really cannot give any useful opinion on the specifics of your case.
Anecdotally, the courts seem to be slower to make property adjustments in favour of men than they do in favour of women, but this is not an area of law in which I practice, so take this (and all other observations above) with a large pinch of salt.
If this is a source of great worry to you, go to a solicitor and get detailed legal advice. I cannot see any solicitor being able to advise you that there is no possibility whatever of a claim, but if the solicitor has full info on your circumstances AND those of your ex-spouse, plus full details on the circumstances of the marriage and separation, you should be able to get a fairly helpful opinion..