  This paper uses statistical and $N$-body methods to explore a new mechanism
to form binary stars with extremely large separations ($> 0.1\,{\rm pc}$),
whose origin is poorly understood. Here, ultra-wide binaries arise via chance
entrapment of unrelated stars in tidal streams of disrupting clusters. It is
shown that (i) the formation of ultra-wide binaries is not limited to the
lifetime of a cluster, but continues after the progenitor is fully disrupted,
(ii) the formation rate is proportional to the local phase-space density of the
tidal tails, (iii) the semimajor axis distribution scales as $p(a)d a\sim
a^{1/2}d a$ at $a\ll D$, where $D$ is the mean interstellar distance, and (vi)
the eccentricity distribution is close to thermal, $p(e)d e= 2 e d e$. Owing to
their low binding energies, ultra-wide binaries can be disrupted by both the
smooth tidal field and passing substructures. The time-scale on which tidal
fluctuations dominate over the mean field is inversely proportional to the
local density of clumps. Monte-Carlo experiments show that binaries subject to
tidal evaporation follow $p(a)d a\sim a^{-1}d a$ at $a\gtrsim a_{\rm peak}$,
known as \"Opik's law, with a peak semi-major axis that contracts with time as
$a_{\rm peak}\sim t^{-3/4}$. In contrast, a smooth Galactic potential
introduces a sharp truncation at the tidal radius, $p(a)\sim 0$ at $a\gtrsim
r_t$. The scaling relations of young clusters suggest that most ultra-wide
binaries arise from the disruption of low-mass systems. Streams of globular
clusters may be the birthplace of hundreds of ultra-wide binaries, making them
ideal laboratories to probe clumpiness in the Galactic halo.
