  We study spherically-symmetric structures in Conformal Gravity and in a
scalar-tensor extension and gain some more insight about these gravitational
theories. In both cases we analyze solutions in two systems: perfect fluid
solutions and boson stars of a self-interacting complex scalar field. In the
purely tensorial (original) theory we find in a certain domain of parameter
space finite mass solutions with a linear gravitational potential but without a
Newtonian contribution. The scalar-tensor theory exhibits a very rich structure
of solutions whose main properties are discussed. Among them, solutions with a
finite radial extension, open solutions with a linear potential and logarithmic
modifications and also a (scalar-tensor) gravitational soliton. This may also
be viewed as a static self-gravitating boson star in purely tensorial Conformal
Gravity.
