  We consider a linear size-structured population model with diffusion in the
size-space. Individuals are recruited into the population at arbitrary sizes.
The model is equipped with generalized Wentzell-Robin (or dynamic) boundary
conditions. This allows modelling of "adhesion" at extremely small or large
sizes. We establish existence and positivity of solutions by showing that
solutions are governed by a positive quasicontractive semigroup of linear
operators on the biologically relevant state space. This is carried out via
establishing dissipativity of a suitably perturbed semigroup generator. We also
show that solutions of the model exhibit balanced exponential growth, that is
our model admits a finite dimensional global attractor. In case of strictly
positive fertility we are able to establish that solutions in fact exhibit
asynchronous exponential growth.
