The trans-actinide, post-actinide or superheavy elements as they are sometimes called are the elements that appear after the actinides, i.e. elements with atomic numbers greater than 102 beginning with lawrencium.  Though all Elements up to 118 have been prepared and new elements are discovered fairly regularly in particle accelerators, theoretical calculations suggest that there is a limit to the size that a nucleus can be.   The same calculations suggest that there is also a limit to the size of an actual atom (i.e. nucleons and electrons), though this is much larger than the atomic nucleus limit.

The trans-actinide elements have been the cause of a spot of bother, not just for the scientists trying to study them, but also for the global scientific establishments trying to agree to there names.  The naming of Element 106, now officially known as Seaborgium (Sg) marked the end of what was known as the "Trans-Fermium Wars", a fiasco of disagreements between the Lawrence Berkeley Laboratory and the American Chemical Society on one side and IUPAC on the other.  The American chemical society wanted the Physicist Glenn Seaborg to receive the honor of having Element 106 named after him.  Unfortunately for the ACS,  at the time Mr. Seaborg wasn't dead and therefore the IUPAC reply to there proposal was "Seaborg had disqualified himself by failing to expire".  In the end the Americans got their way and in 1996 element 106 bears the name of Dr. Seaborg,  who is still alive and well to this day.

 

                           

Dr. Seaborg

Until the existence of a new element is proven to the satisfaction of the International Union of Applied Chemists (IUPAC), the elements are given systematic names.  Once satisfied,  IUPAC names the element, usually after a famous physicist.

The lately IUPAC recommended names for elements 104 - 109 are:

Rutherfordium (Rf, element 104), after physicist Ernest Rutherford 
Dubnium (Db, element 105), after town Dubna 
Seaborgium (Sg, element 106), after nuclear chemist Glenn T. Seaborg 
Bohrium (Bh, element 107), after physicist Niels Bohr 
Hassium (Hs, element 108), after German land "Hessen" 
Meitnerium (Mt, element 109), after physicist Lise Meitner