I just want to know if there is team battles

yes, but they're very rare

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Leader of Team Chronosaber

GENERATION 6: The first time you see this, copy it into your sig on any forum and add 1 to the generation. Social experiment.

People do team-based tournaments of varying configurations, yeah. People also form their own teams locally and here. 
If you want a team tourney, it's worth asking the Organisers in your local scene!