Cook potatoes in pot of boiling salted water until just tender, about 10 minutes. Drain, cool 10 minutes.
Place potatoes in large bowl. Add relish, vinegar and celery seeds; toss to blend. Season generously with salt and pepper. Mix in corned beef, green onions and celery. Mix in enough mayonnaise to bind. Garnish with eggs. Serve immediately or cover and refrigerate up to 1 day.