Assemble each tier: Trim cake level; cut horizontally into 2 layers (10- and 14-inch tiers will have 4 layers). Set 1 layer on same-size foam board. Brush with syrup; spread on puree (see filling amounts below). Then add apricot buttercream (for 10- and 14-inch tiers, repeat with second and third layers). Add top layer. Spread a thin coating of vanilla buttercream over top and sides to seal in crumbs (see coating amounts below); chill until firm, 30 minutes to 1 hour. Then coat each tier with vanilla buttercream; refrigerate.
Stack tiers: insert support dowels in all but the top tier (14": 17 dowels; 12": 13; 10": 13; 8": 5), cutting them to the same height as the finished tier. Stack tiers on cake board. Pipe a pearl border at the base of each tier using vanilla buttercream in a pastry bag with a small round tip, such as Ateco No. 2.
Decorate cake with double ruffles: Let warm to room temperature so buttercream is soft. Cut wafer papers in half lengthwise to make 4-by-11-inch strips. Lightly dampen a paper towel; squeeze to remove any excess moisture. Dampen a wafer-paper strip on both sides with paper towel, and moisten fingertips. Beginning at one end, gather the paper along the center, laying your index finger along the center and folding the ruffles up around it on each side (do not let them touch). Pinch the folds in the paper from the underside, moistening it if necessary so it sticks to itself. Join on new pieces with moistened fingers. While the finished double ruffle is still malleable, press the fold deeply into the soft buttercream of each tier (ruffles that stiffen up can be steamed to soften them). Ruffles may be inserted the night before serving and refrigerated overnight.
Filling amounts: 6-inch tier: 2 teaspoons syrup, 2 tablespoons puree, 1/2 cup apricot buttercream; 8-inch: 1 tablespoon syrup, 1/4 cup puree, 1 cup buttercream; 10-inch: 2 tablespoons syrup (6 tablespoons total), 6 tablespoons puree (1 cup plus 2 tablespoons total), 1 1/4 cups buttercream (3 3/4 cups total); 12-inch: 3 tablespoons syrup, 7 tablespoons puree, 1 1/2 cups buttercream; 14-inch: 1/4 cup syrup (3/4 cup total), 1/2 cup puree (1 1/2 cups total), 1 3/4 cups buttercream (5 1/4 cups total). Coating amounts: 6-inch tier: 1/2 cup vanilla buttercream for crumb coat, plus 1 cup to finish; 8-inch: 3/4 cup, 1 1/2 cups; 10-inch: 1 1/4 cups, 2 cups; 12-inch: 1 1/2 cups, 2 cups; 14-inch: 4 cups, 5 cups.