Besides being scared or angry, what else would make a cat's tail get large?

Well intense love/affection or excitement could tense up muscles in her back and tail causing her fur to fluff up. My cat Shelby fluffs out his fur and shakes his tail (not wags,vibrates more like) when he wants love, and my other cat does when he's playing or somehow energetic/excited so that's probably. Also, I have had a number of kittens who randomly puffed up for no reason, almost as if they didn't know how to control it. :3

Sometimes a cat's tail will puff up when it gets excited about something. I've seen this behavior most often in kittens when they're playing.

we had a huge black cat, but my granddaughter at four years old, thought it was funny to put a hair clip on her tail. She went berserk took off like someone was chasing her, I tried to catch her to take the clip off her tail, but she was too fast for me, scooted out the dog door and it took four runs around the outside of the house, before she slowed down and I could get the clip of her tail, Her tail was indented not fluffed up. :-)

Sometimes my cat does that when she's in a playful mood. She probably just wants your attention and for you to play with her and some yarn or something