Are polarization-entangled photons correlated spatially?

Are polarization-entangled photons correlated spatially?

That is, if I took a pair of entangled photons and looked at their spatial modes with two cameras (one for each photon), would I expect to see correlations between their spatial modes? Does this change depending on if the photons are generated colinearly or not colinearly?

My intuition would be that there is a sort of "momentum conservation" which forces the photons to be anticoorelated in space. Here’s a drawing for a visualization:

EDIT: obviously a polarization entangled state can be written on it’s own without having any other criteria. That is, you can write something like $|Hrangle|Hrangle+|Vrangle|Vrangle$ theoretically, which doesn’t have spatial mode entanglement, but I’m interested in real-life cases.