  The maximum size of a cosmic structure is given by the maximum turnaround
radius -- the scale where the attraction due to its mass is balanced by the
repulsion due to dark energy. We derive generic formulae for the estimation of
the maximum turnaround radius in any theory of gravity obeying the Einstein
equivalence principle, in two situations: on a spherically symmetric spacetime
and on a perturbed Friedman-Robertson-Walker spacetime. We show that the two
formulae agree. As an application of our formula, we calculate the maximum
turnaround radius in the case of the Brans-Dicke theory of gravity. We find
that for this theory, such maximum sizes always lie above the \LCDM value, by a
factor $1 + \frac{1}{3\omega}$, where $\omega\gg 1$ is the Brans-Dicke
parameter, implying consistency of the theory with current data.
