Split Enz (the NZ is a reference to New Zealand, where the band originated) formed in 1973 in Auckland. The founders - Tim Finn and Phil Judd - wanted to create an eclectic pop band; hence the name (which was originally spelled correctly).
During the 1970s, the group went through a myriad of changes, both in terms of style and personnel. The most significant change was Judd's departure; he was replaced by Tim Finn's brother Neil in 1977. During much of this period, Split Enz was a flamboyant art rock band, but they had little success outside of New Zealand and Australia.
This changed with their 1980 release, True Colours, which was something of a coming out party for Neil as a songwriter. The resulting material had a stronger pop sound, and this combined with more straight-forward visuals allowed Split Enz to ride the New Wave (see what we did there?)
True Colours became a #1 album in Australia and New Zealand, and broke into the charts in the U.S. "I Got You" also charted, though it only reached #53 on the U.S. charts. However, it was top 40 in several countries, and hit #1 in Australia and New Zealand.
While the group continued releasing records for the first half of the 1980s, there seemed to be a growing musical disconnect between Tim and Neil, and Tim Finn finally quit the group in 1984. Shortly afterwards, Neil broke up Split Enz and went on to even greater success in Crowded House. The Finn brothers did work together on Crowded House's 1991 LP, Woodface, and more recently as The Finn Brothers.
Cool trivia fact: As mentioned above, Split Enz is a no hit wonder in the U.S.; "I Got You" (#53) was their highest charting single. However, Neil Finn did have two top 40 hits with Crowded House - "Don't Dream It's Over" (#2) and "Something So Strong" (#7).
Cool trivia fact #2: "I Got You" was the 81st video played on MTV's first day; interestingly, it was the third Split Enz video played on MTV, after "History Never Repeats" and "One Step Ahead."