From wikipedia: In January 1997, the newborn baby whale J.J. was found helpless near the coast of Los Angeles, California, 4.2 meters (14 ft) long and 800 kilograms (1,800 lb) in weight. Nursed back to health in SeaWorld San Diego, she was released into the Pacific Ocean on March 31, 1998, 9 meters (30 ft) long and 8,500 kilograms (19,000 lb) in mass. She shed her radio transmitter packs three days later.
Male Killer Whales typically range from 6 to 8 metres (20–26 ft) long and weigh in excess of 6 tonnes (5,443) kilograms.
The average size of adult whale sharks is estimated at 9.7 metres (31.82 ft) and 9 tonnes (20,000 lb)
So sounds like JJ was probably largest than most Killer Whales, but smaller than your average whale shark. However if you just mean largest species of animal kept in captivity than this might be the largest. Gray Whales reach 45 feet (14 m) for adult females (which tend to be slightly larger than adult males). A mature gray whale can reach 40 tonnes. Anyone ever heard of any other young baleen whales kept in captivity?
I believe this was a rare opportunity that has only happened a handful of times. When a stranded young individual (so that they are small enough to manage in captivity) is found and reared back to strength and then hopefully healthy enough to release back into the wild.
Wikipedia says this about Gray Whales in captivity:
" Because of their size and need to migrate, gray whales have rarely been held in captivity, and then only for brief periods of time.
In 1972, a three-month-old gray whale named Gigi (II) was captured for brief study by Dr. David W. Kenney, and then released near San Diego.[48]
In January 1997, the newborn baby whale J.J. was found helpless near the coast of Los Angeles, California, 4.2 meters (14 ft) long and 800 kilograms (1,800 lb) in weight. Nursed back to health in SeaWorld San Diego, she was released into the Pacific Ocean on March 31, 1998, 9 meters (30 ft) long and 8,500 kilograms (19,000 lb) in mass. She shed her radio transmitter packs three days later.[49]"
There isn't any grey whale in captivity at the moment. Displaying large whales would be very difficult for several reasons such as food, space, etc. All baleen whales that were in captivity were rescued animals which died during rahabilitation or were released later. I do not know if a baleen whale has ever been captured with the only purpose of displaying it.
In terms of size, the only species of baleen whale which could be feasibly kept would be the Pygmy right whale, but this is so rare and little-known that this would certainly never happen, even if any institution wanted to attempt it.
