According to wikipedia, regarding the probability of duplicates in random UUIDs:
Only after generating 1 billion UUIDs every second for the next 100 years, the probability of creating just one duplicate would be about 50%. Or, to put it another way, the probability of one duplicate would be about 50% if every person on earth owned 600 million UUIDs.
I guess the same reasoning applies to Java's implementation of UUID. So no, you should not worry about this.
