We present an off-lattice numerical algorithm based upon pure diffusion to construct two-dimensional star-branched polymers with one, three, six and twelve branches. We built up structures with a total of up to 30,000 monomer units. For each one of them averages over one hundred independent configurations were taken. From a finite size analysis the scaling properties of the pair correlation function as well as the radius of gyration were obtained. Our findings indicate that the fractal dimension of the structures are: df=1.21 (0.03) for a linear polymer, df==1.21(0.02), for three branches, df==1.23 (0.02) for six branches and df=1.26 (0.03) for twelve branches.