The Monte Carlo sampling technique is used to investigate the branched structure formation during free-radical polymerization that involves chain transfer to polymer. This method accounts for the history of the generated branched structure and can provide virtually any structural information, because one can observe each polymer molecule directly. In this paper, we investigate the whole molecular weight distribution (MWD) for both pre- and postgelation periods, the MWDs for polymer molecules containing 0, 1, 2, 3, ... branch points, the branching density of polymer molecules as functions of both size and the number of branch points, the spatial distribution of the branched chains at the theta state, etc. Contrary to the term "long-chain" branching, many branch chains are relatively small, and the branched structures formed are significantly different from those usually depicted to introduce "branched polymers" in many introductory textbooks. The radii of gyration at the theta state can be approximated by the Zimm-Stockmayer equation for random branching, in spite of various violations against the assumptions used in deriving the equation.