Thurston introduced emph{invariant (quadratic) laminations} in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polynomials. Important ingredients of his analysis of the angle doubling map $sigma_2$ on the unit circle $mathbb{S}^1$ were the Central Strip Lemma, non-existence of wandering polygons, the transitivity of the first return map on vertices of periodic polygons, and the non-crossing of minors of quadratic invariant laminations. We use Thurstons methods to prove similar results for emph{unicritical} laminations of arbitrary degree $d$ and to show that the set of so-called emph{minors} of unicritical laminations themselves form a emph{Unicritical Minor Lamination} $mathrm{UML}_d$. In the end we verify the emph{Fatou conjecture} for the unicritical laminations and extend the emph{Lavaurs algorithm} onto $mathrm{UML}_d$.
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