  We present an analytical framework to study the first-passage (FP) and
first-return (FR) distributions for the broad family of models described by the
one-dimensional Fokker-Planck equation in finite domains, identifying general
properties of these distributions for different classes of models. When in the
Fokker-Planck equation the diffusion coefficient is positive (nonzero) and the
drift term is bounded, as in the case of a Brownian walker, both distributions
may exhibit a power-law decay with exponent -3/2 for intermediate times. We
discuss how the influence of an absorbing state changes this exponent. The
absorbing state is characterized by a vanishing diffusion coefficient and/or a
diverging drift term. Remarkably, the exponent of the Brownian walker class of
models is still found, as long as the departure and arrival regions are far
enough from the absorbing state, but the range of times where the power law is
observed narrows. Close enough to the absorbing point, though, a new exponent
may appear. The particular value of the exponent depends on the behavior of the
diffusion and the drift terms of the Fokker-Planck equation. We focus on the
case of a diffusion term vanishing linearly at the absorbing point. In this
case, the FP and FR distributions are similar to those of the voter model,
characterized by a power law with exponent -2. As an illustration of the
general theory, we compare it with exact analytical solutions and extensive
numerical simulations of a two-parameter voter-like family models. We study the
behavior of the FP and FR distributions by tuning the importance of the
absorbing points throughout changes of the parameters. Finally, the possibility
of inferring relevant information about the steady-sate probability
distribution of a model from the FP and FR distributions is addressed.
