  Droplets are essential for spatially controlling biomolecules in cells. To
work properly, cells need to control the emergence and morphology of droplets.
On the one hand, driven chemical reactions can affect droplets profoundly. For
instance, reactions can control how droplets nucleate and how large they grow.
On the other hand, droplets coexist with various organelles and other
structures inside cells, which could affect their nucleation and morphology. To
understand the interplay of these two aspects, we study a continuous field
theory of active phase separation. Our numerical simulations reveal that
reactions suppress nucleation while attractive walls enhance it. Intriguingly,
these two effects are coupled, leading to shapes that deviate substantially
from the spherical caps predicted for passive systems. These distortions result
from anisotropic fluxes responding to the boundary conditions dictated by the
Young-Dupr\'e equation. Interestingly, an electrostatic analogy of chemical
reactions confirms these effects. We thus demonstrate how driven chemical
reactions affect the emergence and morphology of droplets, which could be
crucial for understanding biological cells and improving technical
applications, e.g., in chemical engineering.
