Star polymers with intermediate branching functionalities (64 and 128 arms) are known to exhibit a hybrid viscoelastic response, relaxing stress via a fast polymeric arm retraction and a slow colloidal mode. We show that, in the limit of very high functionalities (above 800) and very short arms (3 entanglements or less), the colloidal mode following arm relaxation exhibits a plateau with a modulus much smaller than that expected from the entanglement value and does not relax within the experimentally accessible frequency window. Analysis of the relaxation modes indicates that, even in the melt state, stars with ultrahigh branching functionalities effectively behave like jammed colloids. Their low modulus makes them easily processable, unlike highly entangled linear polymers. A simple state diagram in the melt is proposed with two control parameters: the functionality and the number of entanglements per arm (as a measure of arm size), showing three distinct regimes based on dynamics: polymeric, hybrid polymeric-colloidal, and jammed. These results are briefly discussed in view of other highly branched polymers with density heterogeneities (microgels, bottlebrushes) exhibiting nonterminal solid-like response and supersoft elastomeric features. For the present stars in particular, which are model soft colloids, these findings contribute to the ongoing discussion on jamming in soft matter.