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In this paper, we provide two-sided estimates and uniform asymptotics for the solution of d -dimensional critical fractal Burgers equation u t − Δ α / 2 u + b ⋅ ∇ ( u | u | q ) = 0 , α ∈ ( 1 , 2 ) , b ∈ R d for q = ( α − 1 ) / d and u 0 ∈ L 1 ( R d ) . We consider also q > ( α − 1 ) / d under additional condition u 0 ∈ L ∞ ( R d ) . In both cases we assume u 0 ≥ 0 , which implies that the solution is non-negative. The estimates are given in the terms of the function P t u 0 , where P t denotes the semigroup for the operator ∂ t − Δ α / 2 . [ABSTRACT FROM AUTHOR]