Why is zinc deposited on copper when boiling an aqueous zinc sulfate solution?
Zinc, being in contact with copper, is easily oxidized, because copper drives electrons out of it.

Metallic copper becomes electron-rich and is therefore capable to yield electrons to $\ce{Zn^2+}$ (stemming from $\ce{ZnSO4}$), which reduces to $\ce{Zn^0}$. The latter is finally observed to adsorb at the copper strips.

In other words, copper metal works as an auxiliary electrode whose function is to transport electrons, without being $-$ by no means $-$ transformed during the experiment.

In conclusion, the overall reaction uniquely involves zinc and its ions.

This is similar to what is observed when copper, in contact with zinc, is dipped into an acidic solutions. Hydrogen bubbles are seen even at the copper surface, without the latter being oxidized.