  The goal of this paper is to extend the quiver Grassmannian description of
certain degenerations of Grassmann varieties to the symplectic case. We
introduce a symplectic version of quiver Grassmannians studied in our previous
papers and prove a number of results on these projective algebraic varieties.
First, we construct a cellular decomposition of the symplectic quiver
Grassmannians in question and develop combinatorics needed to compute Euler
characteristics and Poincar\'e polynomials. Second, we show that the number of
irreducible components of our varieties coincides with the Euler characteristic
of the classical symplectic Grassmannians. Third, we describe the automorphism
groups of the underlying symplectic quiver representations and show that the
cells are the orbits of this group. Lastly, we provide an embedding into the
affine flag varieties for the affine symplectic group.
