Heat oven to 350 degrees. Place two racks in center of oven. Butter three 8-by-2-inch round cake pans; line each with a circle of parchment paper. Butter paper, and dust pans with flour; tap out excess. Set aside.
Sift together flour, baking powder, and salt in a medium mixing bowl. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter on medium-low speed until lightened, 1 to 2 minutes. Gradually add sugar; beat until color has lightened, 3 to 4 minutes, scraping down sides of bowl once or twice. Drizzle in eggs, a little at a time, beating on medium-low speed after each addition until batter is no longer slick but is smooth and fluffy, about 5 minutes. Stop to scrape down bowl once or twice so batter will combine well. Beat in vanilla on medium-low speed.
Reduce the mixer speed to low. Alternately add reserved flour mixture and milk, a little of each at a time, beginning and ending with flour mixture. Scrape down the bowl once or twice. Beat in lemon zest, orange zest, lime zest, and 1/3 cup poppy seeds.
Divide batter evenly among the prepared pans. Bake 30 minutes, then rotate pans for even browning. Bake until a cake tester inserted into center of cakes comes out clean, 5 to 10 minutes more. Transfer to wire racks to cool, 15 minutes. Turn out cakes, and set on racks, tops up. Cool completely.
Remove parchment from bottom of each layer. Save best-looking layer for the top. Place one layer on the serving platter. Spread 1 1/2 cups cream-cheese frosting over the top. Place second cake layer on top, and spread remaining 1 1/2 cups frosting over top. Place reserved layer on top. Chill cake, loosely covered with plastic wrap, 1 hour.
To serve, stir lemon glaze well, then pour onto center of top layer of cake, letting it run down the sides. Using a single-hole zester, cut long strips of zest from orange and lemon, if desired. Arrange zest in loose spirals on the top of cake, and sprinkle lightly with poppy seeds.