  We study nonautonomous mappings of the plane by means of spaces of initial
conditions. First we introduce the notion of a space of initial conditions for
nonautonomous systems and we study the basic properties of general equations
that have spaces of initial conditions. Then, we consider the minimization of
spaces of initial conditions for nonautonomous systems and we show that if a
nonautonomous mapping of the plane with a space of initial conditions, and
unbounded degree growth, has zero algebraic entropy, then it must be one of the
discrete Painlev\'{e} equations in the Sakai classification.
