  We study the stationary Navier--Stokes equations in the whole plane with a
compactly supported force term and with a prescribed constant spatial limit.
Prior to this work, existence of solutions to this problem was only known under
special symmetry and smallness assumptions.
  In the paper we solve the key difficulties in applying Leray's {\it invading
domains method} and, as a consequence, prove the existence of $D$-solutions in
the whole plane for arbitrary compactly supported force. The boundary condition
at infinity are verified in two different scenarios: (I) the~limiting velocity
is sufficient large with respect to the external force, (II) both the total
integral of force and the~limiting velocity vanish. Hence, our method produces
large class of new solutions with prescribed spatial limits. Moreover, we show
the uniqueness of $D$-solutions to this problem in a perturbative regime.
  The main tools here are two new estimates for general Navier-Stokes
solutions, which have rather simple forms. They control the difference between
mean values of the velocity over two concentric circles in terms of the
Dirichlet integral in the annulus between them.
