According to Thucydides, when Themistocles was wanted by the Athenians (who probably would have condemned him to death), he took refuge briefly with the king of the Molossians before eventually making his way to the Persian Empire (The Peloponnesian War, book I, chapter 136).
No relation. (I think he mentions it on his website.)
I think the war dogs of Molossus were the forebears of our Great Danes, Mastiffs, etc.