There are a range of legal and tax reasons in certain operating countries why aircraft belonging to leasing companies get registered out-of-country. Particular ones include taxation loopholes, and legal issues that restrict the lessor, particularly if the operating airline defaults on payments or declares bankruptcy. On the other hand some operating countries have restrictions on overseas registrations for crew licencing etc. Things change over time, leading to re-registration.
Ireland is favourite in the EC because of the long association with the old Guinness Peat leasing company, for whom easy registration arrangements were made available. Similarly France has special arrangements which assist Airbus/ATR-manufactured aircraft, a number of which operate with French "overseas" registrations in the F-O... series. Bermuda is another location which is favoured. Different combinations of lessor, manufacturer and operator find different registration administrations suit them.
Italy is a notable operator of out-of-state registrations, but the most widespread nowadays is Russia, where virtually the whole of the Airbus/Boeing fleets acquired by operators there is registered overseas, due to a very substantial import tax on non-Russian manufactured aircraft, which this gets around. Aeroflot is now mostly an Airbus operator, generally registered in Bermuda.