  We study the scaling of ground state entanglement entropy of various free
fermionic models on one dimensional lattices, where the hopping and pairing
terms decay as a power law. We seek to understand the scaling of entanglement
entropy in generic models as the exponent of the power law $\alpha$ is varied.
We ask if there exists a common $\alpha_{c}$ across different systems governing
the transition to area law scaling found in local systems. We explore several
examples numerically and argue that when applicable, the scaling of
entanglement entropy in long-range models is constrained by predictions from
the low-energy theory. In contrast, disordered models and models without a
continuum limit show fractal scaling of entanglement approaching volume-law
behavior as $\alpha$ approaches zero. These general features are expected to
persist on turning on interactions.
