  We revisit the study of the emptiness formation probability, the probability
of forming a sequence of $\ell$ spins with the same ferromagnetic orientation
in the ground-state of a quantum spin chain. We focus on two different
examples, exhibiting strikingly different behavior: the XXZ and Ising chains.
One has a conserved number of particles, the other does not. In the latter we
show that the sequence of fixed spins can be viewed as an additional boundary
in imaginary time. We then use conformal field theory (CFT) techniques to
derive all universal terms in its scaling, and provide checks in free fermionic
systems. These are based on numerical simulations or, when possible,
mathematical results on the asymptotic behavior of Toeplitz and Toeplitz+Hankel
determinants. A perturbed CFT analysis uncovers an interesting $\ell^{-1}\log
\ell$ correction, that also appears in the closely related spin full counting
statistics. The XXZ case turns out to be more challenging, as scale invariance
is broken. We use a simple qualitative picture in which the ferromagnetic
sequence of spins freezes all degrees of freedom inside of a certain "arctic"
region, that we determine numerically. We also provide numerical evidence for
the existence of universal logarithmic terms, generated by the massless field
theory living outside of the arctic region.
