European titles

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Interesting question. I'd be curious to know more about this as well if anyone has first hand experience buying something in Europe.

If boat is Italian and above 10 meter till about 24 meters, what you should be looking for is the Licenzia di Navigazione which should reflect the registration number on the side and the hull number.
In this you will have details of all previous owners. Safeties in Italy on yachts even of small sizes follow a commercial ship like status with RINA inspection needed to be done every 4 years (ships is 2 years).
When RINA expires Italian owners need to bring a surveyor, service the life raft, fire extinguisher, safeties etc etc. This has nothing to do with your purchase.
It is important that the deed of sale be legalized at a Notary or a Public Office department. Cost is double at a notary usually about 2000 EUROS.
Some Registration Offices (you have a lot to chose in Italy; Roma, Viarreggio, Genoa, Venice etc etc) and while all work in a similar pattern, when you request a deletion some have different demands.

For example some offices will give the Permit to delete (nulla osta in Italian) and confirmation of no debits very fast while others may be a bit slower in this regard. They remain in the end Public offices.
Your broker should start to work on this after you accepted the vessel. That is after surveys are done.
If you are foreigner in my experience I would avoid boats owned by the Banks Leasing company, as all are to much of a headache. If private owned and boat has a leasing be sure he can switch it off during a purchase, a clause not every buyer did when in the nice time of 6 - 10 years ago.

May be like that it is less complicated. But beware most new yachts in Italy form 2003 till 2012 where purchased with leasing schemes.
Some advantages for a purchaser as reduced Vat rate and payments which could be done in between three to 10 years.
In my experience most deals where done without the opt out clause, so buyer was stuck to pass the leasing to another Italian citizen to sell or else if you are another EU citizen be ready to play hard.

In leasing defaulted yachts the banks ask some crazy stuff, for example there notary is usually a 4-5k EUROS bill, and sometimes being able to do survey is a very lengthy process if possible.
Anyways some banks in Italy are happy of having yards filled with yachts even though situation has improved in the last two years.

Leasing IMO was the Italian boating industry cancer, from 2005 till 2010.

Not one of the big players for sure. Might be better though.