Zest one of the limes, then juice both limes. You need at least a cup of lime juice, so if your limes are small, it might take three or even four.
Put the lime juice in a non-reactive bowl. The bowl needs to be deep enough to completely submerge the seafood.
Slice the tuna into thin strips, cutting against the grain. Cut the strips to about one inch in length. Salt liberally, then place into the bowl with the lime juice.
If the shrimps aren't already pealed, peal them and remove the tails. Cut the shrimp into bite-sized chunks and place them into the lime juice with the tuna.
Cover the bowl with plasic wrap and refrigerate for a minimum of fifteen minutes and for as long as four hours. The acetic lime juice "cooks" the fish, and the pink salmon will turn white. It's important that the lime juice completely cover the uncooked seafood, since this is what killed any residual bacteria and cooks the fish.
While the seafood marinates, chop the celery. Peal the papaya and the mango, and then chop the fruit into quarter-inch dice. Dice the peppers, onion, and celery. Chop the cilantro. I like lots of cilantro; you might want more or less.
Once the seafood has marinated for fifteen minutes, add the diced fruit and vegetables to the lime juice marinade. Stir to mix well, again being sure that the seafood is submerged.
After another fifteen minutes, peal and dice the avocado. Gently toss it with the seafood mixture. Serve in a small bowl. Garnish with extra cilantro or parsley.