They seem to bundle up a line or two at a time, which would be very small by our standards.
They measure them by train-km I think, and are always specified by the local (Land or city) transport body, leaving the federal transport ministry to deal with long-distance.
Local fares are set locally too, although there are some national schemes which they all support, and all the trains are on the DB web site (bahn.com).
DB Regio wins a good number of the regional concessions, but by no means all.
DB Fernverkehr runs the long distance services under a monopoly licence that is due to end in a few years, and is then due to be tendered competitively.
Don't get the idea that DB is a perfect operation, they are very deep in debt and have an increasingly poor performance record.
There are a few open access long dstance services, but they don't threaten DB in any serious way.
Freight is open access.
An example of a local setup is the Transdev operation around Munich, where they have 3 different operating contracts:
Meridian south east towards Salzburg,
BOB south towards Holzkirchen, and
BRB around Augsburg.
Map below.
https://www.meridian-bob-brb.de/uploads/bb/media_document/43/original.pdf