The conformational and thermodynamic properties of single dendritic linear copolymers are investigated by analytical models and computer simulations. Applying poor solvent conditions on the dendritic part, these molecules are known to form single unimolecular micelle-like structures. A mean-field model applying the Daoud-Cotton approach and a surface tension argument is presented and suggests the splitting of the unimolecular single-core structure into a multicore structure with increasing dendrimers generation and decreasing solvent selectivity. Monte Carlo simulations utilizing the bond fluctuation model with explicit solvent are performed which show the formation of multicore structures for trifunctional codendrimers of different generations and spacer lengths with linear chains attached to the terminal groups. These findings are aimed to understand the physics of spontaneous self-assembly of codendrimers in various well-defined macro-conformations under change of environmental conditions with potential applications such as drug delivery systems.