  Using kinetic Monte Carlo simulations, we show that molecular morphologies
found in non-equilibrium growth can be strongly different from those at
equilibrium. We study the prototypical hybrid inorganic-organic system 6P on
ZnO(10-10) during thin film adsorption, and find a wealth of phenomena
including re-entrant growth, a critical adsorption rate and observables that
are non-monotonous with the adsorption rate. We identify the transition from
lying to standing molecules with a critical cluster size and discuss the
competition of time scales during growth in terms of a rate equation approach.
Our results form a basis for understanding and predicting collective
orientational ordering during growth in hybrid material systems.
