  In this article we deal with different forms of the unique continuation
property for second order elliptic equations with nonlinear potentials of
sublinear growth. Under suitable regularity assumptions, we prove the weak and
the strong unique continuation property. Moreover, we also discuss the unique
continuation property from measurable sets, which shows that nodal domains to
these equations must have vanishing Lebesgue measure. Our methods rely on
suitable Carleman estimates, for which we include the sublinear potential into
the main part of the operator.
