One thing to keep in mind is that growth = filtration. So if it's growing a lot, there is filtration that needs to be done.
I dont trim any of my plants but I have alot of room. My 2 top growers are arrow heads and pothos, with arrowheads being faster. Pothos vines out where as the arrowhead more so "bushes" then vines out. Pothos as they grow you can just wrap them around a stick and they will just go round and round.
Anybody have recommendations for plants that are safe for cats?
arrowheads if you have the height. Mine are in a 4'x2' box, most are over 24" tall
DSCF6018 by smetters20, on Flickr
pothos, ivy or any other vine are really the only other option to make a impact on nitrates and keep in a "compact" area