A theoretical investigation is conducted on a batch free-radical copolymerization in which one type of monomer possesses a high chain transfer constant with a polymerizable double bond in it, which is called the chain transfer monomer. When the chemical structures of the polymerizable double bonds are the same for the monomer pair, the reactivity ratios may be close to unity. In such cases, the probability of possessing a branch point may become the same for all units bound to polymer molecules at any stage of polymerization, irrespective of the magnitude of the chain transfer constant. On the other hand, a homogeneously branched structure cannot be formed except when the chain transfer constant is unity, because the primary chains formed at different stages of polymerization are not connected randomly. The present reaction system could be used to investigate the effect of detailed structural differences on the physical properties of branched polymer systems.