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The selfadjoint extensions of a closed linear relation $R$ from a Hilbertspace ${\mathfrak H}_1$ to a Hilbert space ${\mathfrak H}_2$ are considered inthe Hilbert space ${\mathfrak H}_1\oplus{\mathfrak H}_2$ that contains thegraph of $R$. They will be described by $2 \times 2$ blocks of linear relationsand by means of boundary triplets associated with a closed symmetric relation$S$ in ${\mathfrak H}_1 \oplus {\mathfrak H}_2$ that is induced by $R$. Such arelation is characterized by the orthogonality property ${\rm dom\,} S \perp{\rm ran\,} S$ and it is nonnegative. All nonnegative selfadjoint extensions$A$, in particular the Friedrichs and Kre\u{\i}n-von Neumann extensions, areparametrized via an explicit block formula. In particular, it is shown that $A$belongs to the class of extremal extensions of $S$ if and only if ${\rm dom\,}A \perp {\rm ran\,} A$. In addition, using asymptotic properties of anassociated Weyl function, it is shown that there is a natural correspondencebetween semibounded selfadjoint extensions of $S$ and semibounded parametersdescribing them if and only if the operator part of $R$ is bounded.

Selfadjoint extensions of relations whose domain and range are orthogonal