Is unique id generation using UUID really unique?

I want generate unique ID just like auto increment in java . So previously i used current nano seconds but i end up with clash since two data comes with in same nano seconds .. Does UUID solves the above problem ?

Note :: In my project i can even get 10000 rows of records for each and every minute and I will dump those records along with UIDS in to table .And there may be a situation where i would stop my product and restart it after some time ....So during that situation how could UUID class clarifies the previously generated Uids(which i stored in DB) with the new one going to created(Yet to be dumped in DB) ?