Does using the -arrs use insane amounts of disk space?

The only way I can see switching my Luddite family off of the streaming sites is by making it easier. Up until now, I've torrented the old fashioned way, but now I'm moving into plex (ik, ik, jellyfin is better) and want to start using the -arrs. As I understand it, which I'm not sure I do, the -arrs will automatically grab torrents. In my mind, this would eat up a TB pretty quickly. Do you guys all have massive SSDs (heh), or am I misunderstanding?