Vegeta Jr. is a descendant of Vegeta, seen once at the end of Dragon Ball GT. He is much like Vegeta in name and attitude. He fights in the Tenka-ichi Budkai against Son Goku's great-great grandson, Son Goku Jr.
He is the either the great-great grandson or great grandson of Vegeta and Bulma. He enters a tournament and his challenger is Son Goku Jr. When Vegeta Jr. first sees Goku Jr., he says: "Hey punk, are those rags you're wearing?" He proves to be just like Vegeta. The two competitors are matched equally. Vegeta Jr. lands and goes Super Saiyan and when he sees Goku Jr. do it too, he says "I didn't know we both could go blonde", which leads us to believe that they don't know the actual name for the form.
Note that there is some doubt as to his lineage: he could be descended from either Trunks or Bra, with little evidence providing a substantial case for either. It seems more logical to assume, based on his mother's hair color and the ignorance of the name of Super Saiyan, that he is Bra's grandson, and not Trunks' grandson.