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We propose a new, direct, correlation-free approach based on central momentsof profiles to the asymptotics of width (size of the most abundant level) insome random trees of logarithmic height. The approach is simple but givesprecise estimates for expected width, central moments of the width and almostsure convergence. It is widely applicable to random trees of logarithmicheight, including recursive trees, binary search trees, quad trees,plane-oriented ordered trees and other varieties of increasing trees.

Width and mode of the profile for some random trees of logarithmic height