In a large pot of warm salted water, bring the potatoes to a boil. Cook over moderate heat until tender, 15 minutes; drain.
Meanwhile, in a large, deep skillet, melt the butter in the oil. Add the fennel and cook over moderately high heat, stirring, until browned, about 8 minutes. Add the orange juice and zest. Set the halibut on the fennel; season with salt and pepper. Cover and simmer until the fish is just cooked through, 8 minutes.
Transfer the halibut to plates. Toss the potatoes with the fennel, sprinkle with the tarragon and serve with the fish.
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