We investigate the properties of polymer brushes made of symmetric and asymmetric starlike polymers in good solvent using Langevin dynamics simulations. Two types of populations coexist in such a brush, one of them being made of highly stretched polymers and a second one made of stars that are retracted inside the lower brush regions. Scaling properties of molecular tension, brush layer thickness, and brush density are in reasonable agreement with those of linear chain brushes. The dynamics of stars switching between both the retracted and the stretched states is analyzed, and an exponential scaling with the stretching energy difference is proposed. Most of our results are found in good agreement with recent SCF calculations of Polotsky et al., with one notable exception that their proposed transition from a longest path stretching mode to a uniform stretching mode, the latter being dominant at high densities, has not been supported by our data. Instead, the longest path stretching dominates at high densities as a result of a surface instability, which has previously been found with brushes made of linear chains at high grafting densities.