  We study the phase diagram of fully directed lattice animals with
nearest-neighbour interactions on the square lattice. This model comprises
several interesting ensembles (directed site and bond trees, bond animals,
strongly embeddable animals) as special cases and its collapse transition is
equivalent to a directed bond percolation threshold. Precise estimates for the
animal size exponents in the different phases and for the critical fugacities
of these special ensembles are obtained from a phenomenological renormalization
group analysis of the correlation lengths for strips of width up to n=17. The
crossover region in the vicinity of the collapse transition is analyzed in
detail and the crossover exponent $\phi$ is determined directly from the
singular part of the free energy. We show using scaling arguments and an exact
relation due to Dhar that $\phi$ is equal to the Fisher exponent $\sigma$
governing the size distribution of large directed percolation clusters.
