We consider a model to describe starlike polymers featuring a steric repulsion accompanied by a dispersion- or depletion-induced tunable attraction. The range and depth of the latter can be controlled by suitable choices of the solvent, salt concentration and/or depletant size and type, whereas the strength of the steric repulsions is set by the arm number
of the stars. We focused on star polymers with arm number
=32. Depending on the choice of the attraction characteristics and on the temperature, the system exhibits, in addition to the usual ultra-soft repulsion, a relatively short range barrier at longer distances. Our results show a variety of structurally distinct states. In the fluid phase we find evidence for cluster formation which is accompanied by fluid-phase separation. Moreover the system presents unexpected fluid-solid transitions which are
for the purely repulsive case. The dependence of the cluster and solid regions, and the location of the critical point on the potential parameters is quantitatively analyzed.