Thoroughly rinse and dry the squid rings and tentacles on cloth towels. In a large heavy pot heat 2 tablespoons olive oil over moderate heat. Cook the onion until translucent. Add the garlic and thyme and cook for 1 minute. Add the squid and cook for 2 minutes. Add the tomatoes and wine and bring the mixture to a simmer. Cover the pot and leave barely at a simmer over low heat for 45 minutes or transfer the pot, once the liquid has come to a simmer, to a 300-degree oven and bake for 45 minutes to 1 hour.
While the squid is cooking, cut the top 2/3 off the artichokes, trim the dark leaves off the bottoms and sides, and put the artichokes in a non-aluminum pot with lemon juice, a tablespoon of olive oil and enough water to cover generously. Simmer the artichokes until they are just tender when poked through the bottom with a knife, about 15 minutes for baby artichokes or 30 minutes for large artichokes. Drain and let cool. If you're using large artichokes, carefully pull out the choke with a tablespoon and cut the artichoke bottoms into 5 wedges each. Trimmed baby artichokes can be left whole or cut in half. Toss the cooked artichoke bottoms or baby artichokes in a tablespoon of olive oil with salt and pepper.
Put the pearl onions and remaining olive oil in a small pot just large enough to hold the onions in a single layer. Add enough water to come halfway up the onions, partially cover the pot, and simmer the onions for about 15 minutes, until all the water evaporates and leaves them with a light glaze. Uncover the squid and, if necessary, boil the liquid until slightly thickened. Add the artichokes and pearl onions, stirring to combine. Season with salt and pepper to taste. Stir in the olives and the chopped parsley.