The true extent of Zzigg's power is unknown, but having traveled to the Dark Continent with Isaac Netero, he must have possessed a great deal of strength and survival skills. He has most likely received the traditional Zoldyck training.
In the Chapter 344, along with Isaac Netero's and Linne Hors-d'oeuvre's alternate names, Zzigg's name is revealed and written as "Zzigg Za＋〇ldyeck"—with his surname exactly like the name of the Zoldyck family is spelled in the 2004 Databook, using an unknown symbol resembling a crossed circle instead of an "o" (identical to the "ho" syllable in the Hunter × Hunter Alphabet).
In Viz's translation of Volume 33, his name is spelled as "Zigg Zzoldyck".
It is widely speculated that Zzigg is Maha's son and Zeno's father, both due to the generational graph and the timing of Netero's expedition. On the other hand, due to him looking rather different from the man portrayed in the graph, Zzigg could also be from Maha's generation, or be his son but not Zeno's father. The two may even be the same person, if Maha's name was retconned along with his age.
Although, it should be noted if Zzigg actually were to be Zeno's father, it would make sense that the man portrayed in the graph is what Zzigg may currently look like in his old age in the present timeline of the series, as shown with Maha, Zeno, and Silva who are portrayed in their current age on the graph.