It is claimed that the Catholic church owns 20% of all real estate in Italy, and a quarter of all real estate in Rome. Read here. Even assuming this is the lump sum for all the parishes (not just the Holy See), is this figure in the right ballpark?
Both data are mentioned in several media articles. Two of the most authoritative seem to be a 2010 article on Il Giornale and especially a 2013 article on the financial newspaper Il Sole 24 Ore.
Both attribute the 20% datum (circa il 20% del patrimonio immobiliare in Italia è in mano alla Chiesa, “about 20% of the real estate in Italy is in the hands of the Church”) to the Gruppo Re (a company assisting clergy members in financial activities: see here): se a metà degli anni novanta i beni delle missioni si aggiravano intorno agli 800 miliardi di vecchie lire, oggi dovrebbero valere dieci volte di più. Il patrimonio nazionale immobiliare della Chiesa raggiunge quasi il 22 per cento del totale italiano, proprietà all’estero escluse (“if in mid-1990s the missions' possessions amounted to about 800 billions Lire, now they should be worth ten times as much. The national real estate of the Church comprises almost 22% of the Italian total, excluding the possessions abroad”, in the cited article from Il Giornale).
As for the 25% datum about Rome, Il Sole 24 Ore (as well as other sources) quotes una storica inchiesta che Paolo Ojetti pubblicò sull'Europeo nel lontano 1977 dove riuscì per la prima volta a calcolare che un quarto della città di Roma era di proprietà della Chiesa (“a historical report that Paolo Ojetti published back in 1977 in L'Europeo, where he managed for the first time to reckon that a quarter of the city of Rome belonged to the Church”).
According to Italian Society Reflected in New Vatican Accord, Toledo Blade, 14 October 1984, page 2 of section C:
The Vatican owns 1.8 million acres and an undisclosed number of buildings, apartments and palazzi all over Italy.
So just based upon land area, between 2 and 3%.
See also the US government publication Land Redistribution: One Aspect Of Agrarian Reform in Italy in Foreign agriculture : a review of foreign farm policy, production, and trade, October 1949:
No land will be taken from the 1.1 million acres owned directly by the church and by religious orders, the 667,170 acres owned by welfare agencies, nor from the 2.1 million acres owned by resettlement agencies, nonprofit corporations, and the so-called agrarian associations.
This article cites to Giuseppi Medici— "La Distribuzione della Proprieta Fondiaria in Italia," Volume II, page 46, Institute Nazionale di Economia Agraria, Roma, October 1948.