  The master field is the large $N$ limit of the Yang-Mills measure on the
Euclidean plane. It can be viewed as a non-commutative process indexed by paths
on the plane. We construct and study generalized master fields, called free
planar Markovian holonomy fields, which are versions of the master field where
the law of a simple loop can be as more general as it is possible. We prove
that those free planar Markovian holonomy fields can be seen as well as the
large $N$ limit of some Markovian holonomy fields on the plane with unitary
structure group.
