  We define generic ensembles of infinite trees. These are limits as
$N\to\infty$ of ensembles of finite trees of fixed size $N$, defined in terms
of a set of branching weights. Among these ensembles are those supported on
trees with vertices of a uniformly bounded order. The associated probability
measures are supported on trees with a single spine and Hausdorff dimension
$d_h =2$. Our main result is that their spectral dimension is $d_s=4/3$, and
that the critical exponent of the mass, defined as the exponential decay rate
of the two-point function along the spine, is 1/3.
