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The only survivor from the original Zilla's eggs(before "Godzilla: Final Wars" all Zillas were called Godzilla). Unlike his parent though he gets incredibly violent when threatened or when something bad is going to happen.
At the end of the film a lone egg is seen to have survived the bombing before it hatches, it is assumed to be Zilla Jr..
Godzilla: The Series
Nick Tatopoulos along with the army search for any surviving newborn Zillas. Nick later falls through a hole finding a surviving egg which hatches revealling Zilla Jr.. Zilla Jr. then inspects Nick and imprints on Nick reconizing the smell of the original Zilla on Nick. Zilla Jr. then flees in fear from some stray sparks from a wire. Nick not telling the army about Zilla Jr. and later on trys to capture him for study with some others. The attempt fails but Zilla Jr. stays anyway believing Nick as his parent. The military now aware of Zilla Jr.'s presence attacks himfor believing he is the cause of people disappearing in Jamaica. The military believing they've killed him leave. Zilla Jr. later on reappears in Jamaica protecting Nick from Crustaceous Rex. The military the came and seeing what Zilla Jr. did allowed him to live.
Godzilla: Final Wars
It's probably not Zilla Jr. because he is immune to mind control under normal conditions as well as a better fighter then all previous Zillas. So it is probably a new character but there is no real evidance to support this.