In this work, the transition between diffusion-limited (DLA) and ballistic aggregation (BA) models was reconsidered using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter lambda, which assumes the value lambda=0 (1) for the ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, an efficient algorithm was developed. For lambda (not equal to) 0 , the patterns are fractal on small length scales, but homogeneous on large ones. We evaluated the mean density of particles (-)rho in the region defined by a circle of radius r centered at the initial seed. As a function of r, (-)rho reaches the asymptotic value rho(0)(lambda) following a power law (-)rho = rho(0) +Ar(-gamma) with a universal exponent gamma=0.46 (2) , independent of lambda . The asymptotic value has the behavior rho(0) approximately |1-lambda|(beta) , where beta=0.26 (1) . The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by xi approximately |1-lambda|(-nu) , where nu=0.61 (1) , while the cluster mass at the crossover follows a power law M(xi) approximately |1-lambda(-alpha) , where alpha=0.97 (2) . We deduce the scaling relations beta=nugamma and beta=2nu-alpha between these exponents.