I do not know if this might be of any help, I only know what was told by my mother and aunts, I will try to deepen into this:
My Great-Grand father Giaccomo Agostini came along to the shores of Carupano, a very small town on the shores of eastern Venezuela, in the migration of the 30's. My mother sustains that he was politically prosecuted because he was an Anarchist. He never learned to speak spanish well and according to my mother he had a very thick french accent. I do believe that he wanted to get out of Corsica, and the reason being (this is my own speculation) that my mother or even my grandfather for that matter never master their language of ancestry (I really think Giaccomo spoke some french-italian dialect). In fact I do believe they came to South America trying to start a new life, disconnecting themselves from their motherland but then again I have nothing to back these ideas. We the remaining Agostini have grown, and we ourselves have started to spread. My brothers and I, as well as my cousins on all my aunt's side will be the last Agostini, all our sons and daughters will inherit only the father's side last name. But on my uncle's side, I have four cousins that eventually will let the Agostini name live on (now some of them have married and one of them has on child). It has been a pleasure to have written back, and please feel free to write at my e-mail address.