  We generalize the uniform spanning tree to construct a family of
determinantal measures on essential spanning forests on periodic planar graphs
in which every component tree is bi-infinite. Like the uniform spanning tree,
these measures arise naturally from the laplacian on the graph.
  More generally these results hold for the "massive" laplacian determinant
which counts rooted spanning forests with weight $M$ per finite component.
These measures typically have a form of conformal invariance, unlike the usual
rooted spanning tree measure. We show that the spectral curve for these models
is always a simple Harnack curve, this fact controls the decay of edge-edge
correlations in these models.
  We compute a limit shape theory in these settings, where the limit shapes are
defined by measured foliations of fixed isotopy type.
