  In the context of Brans--Dicke theories, eternal inflation is described in
such a way that the evolution of the inflaton field is determined by the value
of the Planck mass in different regions of the universe. The Planck mass is
given by the values of the Brans--Dicke field, which is coupled to the scalar
curvature in the Lagrangian. We first calculate the joint probability
distributions of the inflaton and Brans--Dicke fields, in order to compute the
3--volume ratios of homogeneous regions with arbitrary values of the fields
still undergoing inflation with respect to thermalized regions. From these
volume ratios one is able to extract information on the values of the fields
measured by a typical observer for a given potential and, in particular, the
typical value of the Planck mass at the end of inflation. In this paper, we
investigate volume ratios using a regularization procedure suggested by
Vilenkin, and the results are applied to powerlaw and double--well potentials.
The spectrum of density fluctuations is calculated for generic potentials, and
we discuss the likelihood of various scenarios that could tell us whether our
region of the universe is typical or untypical depending on very general bounds
on the evolution of the Brans--Dicke field.
