Making a Will
Your Italian property falls under the Italian law of succession unless you stipulate that the property should be left according to your foreign will. Your foreign will can take precedence if you are not resident in Italy, and it falls under the legislation of the country where you pass the majority of your life.
However to be valid in Italy the will must be published in Italy - which means a notary making the will a public act (with all the inherent costs). Only then can the Italian succession be done which transfers the name of ownership into that of the heir stipulated in the will.
Without a published will, or if you die intestate, the property will divided according to the Italian 'legittima' whereby the property is divided into quotas between spouse, children, parents etc depending on who's around at the time.
For the sake of clarity, and not to leave a mess for those already grieving, it is much easier to make a will, or at least leave a holographic will in ITaly saying you would like the law of your home country to take precedence.
Likewise, if you don't want to be buried in Italy, you should write something to that effect and sign it (in longhand) and make sure it can be found easily. Cremation and repatriation require signatures and forms which if it isnt clear that it was the will and intention of the defunct can cause delays and stress for all concerned.