  Surface growth, by association or dissociation of material on the boundaries
of a body, is ubiquitous in both natural and engineering systems. It is the
fundamental mechanism by which biological materials grow, starting from the
level of a single cell, and is increasingly applied in engineering processes
for fabrication and self-assembly. A significant complexity in describing the
kinetics of such processes arises due to their inherent coupled interaction
with the diffusing constituents that are needed to sustain the growth, and the
influence of local stresses on the growth rates. Moreover, changes in
concentration of solvent within the bulk of the body, generated by diffusion,
can affect volumetric changes, thus leading to an additional interacting growth
mechanism. In this paper we present a general theoretical framework that
captures these complexities to describe the kinetics of surface growth while
accounting for coupled diffusion. Then, by combination of analytical and
numerical tools, applied to a simple growth geometry, we show that the
evolution of such growth processes rapidly tends towards a universal path that
is independent of initial conditions. This path, on which surface growth
mechanisms and diffusion act harmoniously, can be extended to analytically
portray the evolution of a body from inception up to a treadmilling state, in
which addition and removal of material are balanced.
