  In this work, the transition between diffusion-limited and ballistic
aggregation models was revisited 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 ballistic
(diffusion-limited) aggregation model. Patterns growing from a single seed were
considered. In order to simulate large clusters, a new efficient algorithm was
developed. For $\lambda \ne 0$, the patterns are fractal on the small length
scales, but homogeneous on the large ones. We evaluated the mean density of
particles $\bar{\rho}$ in the region defined by a circle of radius $r$ centered
at the initial seed. As a function of $r$, $\bar{\rho}$ reaches the asymptotic
value $\rho_0(\lambda)$ following a power law $\bar{\rho}=\rho_0+Ar^{-\gamma}$
with a universal exponent $\gamma=0.46(2)$, independent of $\lambda$. The
asymptotic value has the behavior $\rho_0\sim|1-\lambda|^\beta$, where $\beta=
0.26(1)$. The characteristic crossover length that determines the transition
from DLA- to BA-like scaling regimes is given by $\xi\sim|1-\lambda|^{-\nu}$,
where $\nu=0.61(1)$, while the cluster mass at the crossover follows a power
law $M_\xi\sim|1 -\lambda|^{-\alpha}$, where $\alpha=0.97(2)$. We deduce the
scaling relations $\beta=\n u\gamma$ and $\beta=2\nu-\alpha$ between these
exponents.
