  We study the volume of extrinsic balls and the capacity of extrinsic annuli
in minimal submanifolds which are properly immersed with controlled radial
sectional curvatures into an ambient manifold with a pole. The key results are
concerned with the comparison of those volumes and capacities with the
corresponding entities in a rotationally symmetric model manifold. Using the
asymptotic behavior of the volumes and capacities we then obtain upper bounds
for the number of ends as well as estimates for the fundamental tone of the
submanifolds in question.
