  Secrecy and security are crucial in communication. So, quantum secret sharing
protocol has recently been proposed to distribute a secret message to a set of
parties, where the decoding procedure is forbidden individually, and a
cooperative operation is needed. For this, quantum steering as an intriguing
kind of nonlocality, is proven to be a useful resource for efficient
implementations of the QSS protocol. Here, we study the distribution of
Gaussian steering over an asymmetric three-mode optomechanical state. We show
that a single-mode cannot be jointly steered by the two others, and further
verify the monogamy inequalities of Gaussian steering. The state at hand
displays genuine tripartite steering. Also, we observe one-way steering in the
configuration (1vs1) mode as well as (1vs2) mode, hence, we reveal that the
asymmetry introduced into the state we consider, is a necessary condition but
not sufficient for reaching one way steering. As well, we detect one-way
steering between two modes never directly interact. Strikingly, our model
exhibits an extreme level of steering, where two single-mode cannot steer
individually the third mode, while, they can collectively, which is decisive
for practical execution of the QSS protocol.
