While the mass transport mechanisms and dynamics of molecular precursors, ultrathin films that precede spreading droplets, are well understood, the requirements for their formation and the reasons for the occurrence of different precursor shapes remain unclear. In this work, we study these requirements using molecular dynamics simulations of spreading droplets and extensive free energy computations. For a simple simulation model, we demonstrate that with growing droplet substrate attraction, spreading passes succesively through regimes with no precursor, a monolayer precursor, and a continuously growing precursor. We show that the onset of layer formation and the changes in the precursor shape correlate with the free energy of layer formation. On the basis of these findings, we show that a positive spreading coefficient is sufficient but not necessary for precursor formation.