  This work considers lattice walks restricted to the quarter plane, with steps
taken from a set of cardinality three. We present a complete classification of
the generating functions of these walks with respect to the classes algebraic,
transcendental holonomic and non-holonomic. The principal results are a new
algebraic class related to Kreweras' walks; two new non-holonomic classes; and
enumerative data on some other classes. These results provide strong evidence
for conjectures which use combinatorial criteria to classify the generating
functions all nearest neighbour walks in the quarter plane.
