Puree first 5 ingredientsin blender until smooth. With machinerunning, gradually add vegetable oil,then olive oil. Season to taste with saltand pepper. DO AHEAD: Can be made 1 dayahead. Cover and chill.
Cook asparagus in large skilletof boiling salted water until just tender,4 to 5 minutes.
Transfer asparagus to13x9x2-inch pan of ice water to cool.
Drainasparagus and pat dry. DO AHEAD: Can bemade 8 hours ahead. Wrap in paper towels,then plastic, and chill.
Place potatoes in large saucepan.
Addenough water to cover potatoes by 1 inch.
Sprinkle with salt. Bring to boil and cookuntil potatoes are tender, 10 to 15 minutes,depending on size of potatoes.
Drain; letcool 5 minutes.
Place in medium bowl.
Add1/4 cup vinaigrette; toss to coat. Season totaste with salt and pepper.
Heat olive oil in small skillet overmedium-high heat.
Add capers and fryuntil capers are crisp and open like flowers,stirring often, 45 to 60 seconds. Usingslotted spoon, transfer capers to papertowels to drain. DO AHEAD: Potatoes andcapers can be made 2 hours ahead.
Letstand at room temperature.
Place asparagus in large bowl.
Add 2tablespoons vinaigrette and toss to coat.Toss potatoes again to coat, adding 1 moretablespoon vinaigrette if dry.
Place greensand radishes in another large bowl. Tosswith enough vinaigrette to coat.
Spreadgreens and radishes over large platter.Arrange potatoes, asparagus, eggs, andtuna atop greens.
Drizzle some vinaigretteover tuna.
Sprinkle with fried capers andchive blossoms, if desired.
