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My stromanthe has thin roots coming out of the bottom of the pot and I was wondering if this is the sort of plant that likes to be potbound or not as I'd rather not have to repot if not really necessary.

I doubt it likes to be pot bound. You generally only let things become pot bound to stress them into fruiting or flowering (like figs for instance). As this seems to be a foliage plant I'm guessing it would prefer room to grow.

I didn't realise that was only to do with fruiting. It has now been repotted into a larger pot - it should keep it comfy for a while.