  We derive inequalities sufficient to detect the genuine $N$-partite steering
of $N$ distinct systems. Here, we are careful to distinguish between the
concepts of full $N$-partite steering inseparability (where steering is
confirmed individually for all bipartitions of the $N$ systems, thus negating
the bilocal hidden state model for each bipartition) and genuine $N$-partite
steering (which excludes all convex combinations of the bilocal hidden state
models). Other definitions of multipartite steering are possible and we derive
inequalities to detect a stricter genuine $N$-partite steering based on only
one trusted site. The inequalities are expressed as variances of quadrature
phase amplitudes and thus apply to continuous variable systems. We show how
genuine $N$-partite steerable states can be created and detected for the nodes
of a network formed from a single-mode squeezed state passed through a sequence
of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if
one uses two squeezed inputs, or $N$ squeezed inputs. We are able to confirm
that genuine tripartite steering (by the above definition and the stricter
definition) has been realised experimentally. Finally, we analyze how bipartite
steering and entanglement is distributed among the systems in the tripartite
case, illustrating with monogamy inequalities. While we use Gaussian states to
benchmark the criteria, the inequalities derived in this paper are not based on
the assumption of Gaussian states, which gives advantage for quantum
communication protocols.
