  In this paper we present several set of solutions of static and spherically
symmetric solitonic boson stars. Each set is characterized by the value of
{\sigma} that defines the solitonic potential in the complex scalar field
theory. The main features peculiar to this potential occur for small values of
{\sigma}, but for which the equations become so stiff as to pose numerical
challenges. Without making approximations we build the sets for decreasing
{\sigma} values and show how they change their behavior in the parameter space,
giving special attention to the region where thin-wall configurations dwell.
The validity of the thin-wall approximation is explored as well as the
possibility of the solution sets being discontinuous. We investigate five
different possible definitions of a radius for boson stars and employ them to
calculate the compactness of each solution in order to assess how different the
outcomes might be.
