Sprinkle the turbot on both sides with salt and pepper. Heat a few tablespoons of canola oil in a large saute pan over high heat. When you see a wisp of smoke, add the fillets to the pan (do not overcrowd the pan to achieve a proper sear, so cook in batches if you have to). Add 1 to 2 tablespoons of the butter per fillet to the pan. Cook the turbot on both sides until lightly golden brown and just cooked through, about 2 minutes total. Remove to a plate.
Deglaze the pan with the white wine over medium-high heat and let cook all the way down to a dry pan. Add the remaining butter to the saute pan and cook until slightly golden brown. Add the capers and lemon juice, and then add the fish back to the pan. Baste the fish with some of the sauce to warm. Remove from heat, add the tarragon and season with salt and pepper if necessary.
Put each fillet on a plate and spoon the sauce over the fish. Garnish with the lemon zest and a sprig of tarragon.