  Monogamy inequalities for the way bipartite EPR steering can be distributed
among N systems are derived. One set of inequalities is based on witnesses with
two measurement settings, and may be used to demonstrate correlation of
outcomes between two parties, that cannot be shared with more parties. It is
shown that the monogamy for steering is directional. Two parties cannot
independently demonstrate steering of a third system, using the same
two-setting steering witness, but it is possible for one party to steer two
independent systems. This result explains the monogamy of two-setting Bell
inequality violations, and the sensitivity of the continuous variable (CV) EPR
criterion to losses on the steering party. We generalise to m settings. A
second type of monogamy relation gives the quantitative amount of sharing
possible, when the number of parties is less than or equal to m, and takes a
form similar to the Coffman-Kundu-Wootters (CKW) relation for entanglement. The
results enable characterisation of the tripartite steering for CV Gaussian
systems and qubit GHZ and W states.
