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The tiny graviton Matrix theory \cite{tiny} is proposed to
describe DLCQ of type IIB string theory on the maximally
supersymmetric plane-wave or $AdS_5\times S^5$ background. In this
paper we provide further evidence in support of the tiny graviton
conjecture by focusing on the zero energy, half BPS configurations
of this matrix theory and classify all of them. These vacua are
generically of the form of various three sphere giant gravitons.
We clarify the connection between our solutions and the half BPS
configuration in $\N=4$ SYM theory and their gravity duals.
Moreover, using our half BPS solutions, we show how the tiny
graviton Matrix theory and the mass deformed $D=3,\ {\N}=8$
superconformal field theories are related to each other.
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