The purpose of this study was to use polynomial regression analyses to examine the torque- and power-velocity relationships and calculate and compare the vertices of these nonlinear models, and how they relate to measurements of muscle size and maximal strength, between male and female children and adolescents during maximal isokinetic leg extension muscle actions. Sixteen children (n = 8 males, n = 8 females) and 22 adolescents (n = 11 males, n = 11 females) participated in this study. Measurements of growth included age, maturity offset, height, body mass, fat-free mass, and quadriceps femoris muscle cross-sectional area (CSA). Participants completed maximal voluntary isometric contractions (MVICs) of the leg extensors and maximal voluntary isokinetic leg extensions at 60, 120, 180, 240, and 300°·s-1. Variables calculated during all leg extension muscle actions included peak torque (PT, Nm) and mean power (MP, W). Polynomial regression analyses determined the model of best fit for the PT- and MP-velocity relationships. For each participant, the vertex from the PT- and MP-velocity quadratic models were quantified as the predicted maximum velocity of last measurable torque (VPT) and the predicted velocity of maximum mean power (VMP), respectively. Measurements of growth, PT and MP at all velocities, VPT, and VMP were greater in the adolescents than children. When normalized to CSA, VPT and VMP remained greater for adolescents than children, and exhibited low to very high relationships with measurements of growth. When normalized to MVIC strength, VPT and VMP were no longer different between children and adolescents and exhibited negligible to low relationships with measurements of growth. The results of the present study suggest that the ability to produce torque and power at high velocities may be more dependent on muscle strength than muscle size, which suggests that mechanisms other than muscular hypertrophy affect torque and power production at high velocities in young males and females.