Unless it says “in fee” against immediate lessor, you should assume your ancestors were renting. The big change came with the Land Purchase Act in 1903 (often referred to as Wyndham’s Land Act) which allowed people to buy land and property with a government mortgage. The sale was obviously still subject to the owner’s consent but this was often given. Your ancestors may have bought their land at this time. Griffiths Revaluation records are the place to look to see when they purchased their property.(They are not on-line). For the Republic these are held in the Valuation office, Dublin. For Northern Ireland they are in PRONI. When the property became theirs it will be described as “in fee” in the revaluation records, as I explained previously, and if that was as a result of a Land Purchase Act mortgage post 1903, there will be a little red stamp with “LAP” beside it (Land Act purchase) in the Griffiths records.