We study neutrino masses and mixing in R-parity violating supersymmetric
models with generic soft supersymmetry breaking terms. Neutrinos acquire masses
from various sources: Tree level neutrino--neutralino mixing and loop effects
proportional to bilinear and/or trilinear R-parity violating parameters. Each
of these contributions is controlled by different parameters and have different
suppression or enhancement factors which we identified. Within an Abelian
horizontal symmetry framework these factors are related and specific
predictions can be made. We found that the main contributions to the neutrino
masses are from the tree level and the bilinear loops and that the observed
neutrino data can be accommodated once mild fine-tuning is allowed.Comment: 18 pages; minor typos corrected. To be published in Physical Review