  In this work, we consider a specific space of foliations with $C^1$ leaves
and H\"older holonomies of the square $M=[0,1]^2$, with some topology and we
show that a generic such foliation is non-absolutely continuous, furthermore,
the conditional measures defined by Rokhlin disintegration are Dirac measures
on the leaves. This space of foliations is motivated by the foliations that
appear in hyperbolic systems and partially hyperbolic systems.
