  The $\Gamma$-convergence of lower bounded quadratic forms is used to study
the singular operator limit of thin tubes (i.e., the vanishing of the cross
section diameter) of the Laplace operator with Dirichlet boundary conditions; a
procedure to obtain the effective Schr\"odinger operator (in different
subspaces) is proposed, generalizing recent results in case of compact tubes.
Finally, after scaling curvature and torsion the limit of a broken line is
briefly investigated.
