Step 1Heat the olive oil in a wide, deep saute pan over medium-high heat. Pat the poussin completely dry with paper towels. Season well on both sides with salt and pepper. Lay into the pan skin side down and cook until browned, about 3 minutes, then turn (taking care not to tear the skin) and brown the flesh side, about 2 minutes. Transfer to a warm platter.
Step 2Pour off and discard all but 1 tablespoon of the fat in the pan. Add the ramps and celery. Sprinkle with salt and pepper. Cook, stirring, until the vegetables are softened, about 2 to 3 minutes. Add the wine and cook, stirring, until the liquid is reduced by half. Return the poussin to the pan. Pour the stock around them, avoiding the skin. Lower the heat to a simmer, cover the pan and cook 10 minutes.
Step 3While the poussin stew, melt the butter in a small saute pan over medium heat. Add the morels, season with salt and pepper and saute, stirring often, for 8 to 10 minutes. Remove the morels from the pan with a slotted spoon and set aside. Sprinkle the flour over the butter remaining in the pan and cook, stirring constantly, for 2 minutes.
Step 4When the poussin are done, arrange the asparagus tips around them in the pan, cover and cook about 3 minutes, or until the juices run clear when the leg of one poussin is pricked (remove the asparagus if it starts to overcook). Transfer the birds and the asparagus to a serving platter. Arrange the morels around the chicken.
Step 5Whisk the flour mixture into the cooking liquid and cook, whisking, until the liquid thickens into a light sauce. Stir in the tarragon. Spoon over the poussin and serve.