  We study the typical behavior of the harmonic measure of balls in large
critical Galton-Watson trees whose offspring distribution has finite variance.
The harmonic measure considered here refers to the hitting distribution of
height $n$ by simple random walk on a critical Galton-Watson tree conditioned
to have height greater than $n$. We prove that, with high probability, the mass
of the harmonic measure carried by a random vertex uniformly chosen from height
$n$ is approximately equal to $n^{-\lambda}$, where the constant $\lambda>1$
does not depend on the offspring distribution. This universal constant
$\lambda$ is equal to the first moment of the asymptotic distribution of the
conductance of size-biased Galton-Watson trees minus 1.
