  We study the free data in the Fefferman-Graham expansion of asymptotically
Einstein metrics with non-zero cosmological constant. We prove that if
$\mathscr{I}$ is conformally flat, the rescaled Weyl tensor at $\mathscr{I}$
agrees up to a constant with the free data at $\mathscr{I}$ , namely the
traceless part of the $n$-th order coefficient of the expansion. In the
non-conformally flat case, the rescaled Weyl tensor is generically divergent at
$\mathscr{I}$ but one can still extract the free data in terms of the
difference of the Weyl tensors of suitably constructed metrics, in full
generality when the spacetime dimension $D$ is even and provided the so-called
obstruction tensor at $\mathscr{I}$ is identically zero when $D$ is odd. These
results provide a geometric definition of the data, particularly relevant for
the asymptotic Cauchy problem of even dimensional Einstein metrics with
positive $\Lambda$ and also for the odd dimensional analytic case
irrespectively of the sign of $\Lambda$. We establish a Killing initial data
equation at spacelike $\mathscr{I}$ in all dimension for analytic data. These
results are used to find a geometric characterization of the Kerr-de Sitter
metrics in all dimensions in terms of its geometric data at null infinity.
