The Essential Norm of a Bloch-to-$Q_p$ Composition Operator The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are subspaces of $\BMOA$ for $0 Keywords:Bloch space, little Bloch space,$\BMOA$,$\VMOA$,$Q_p\$ spaces,, composition operator, compact operator, essential normCategories:47B38, 47B10, 46E40, 46E15