Preheat oven to 450°. On a rimmed baking sheet, toss potatoes and artichokes (do not fully drain artichokes; use a little of their marinade for flavoring potatoes) with 1/8 c olive oil and sprinkle generously with salt and pepper. Roast 18 min, tossing halfway through, until golden brown. Push all to one side of pan.
Add halibut and asparagus to pan, drizzling with remaining olive oil, salt and pepper. Return all to oven and bake until fish filets are cooked through, 8 min.
Meanwhile combine mayonnaise with half of lemon juice, zest and half of basil. Taste and add pinch of salt and pepper. When ready to serve, arrange potatoes, asparagus, artichoke hearts and fish on platter. Top with olives, basil, capers and remainder of lemon juice. Serve with lemon basil mayo on side.