Can somebody help me with an option to randomly assign polygons of specific size to a study area/ a spatial extend using arcGIS?
You could use this tool:
https://pro.arcgis.com/en/pro-app/latest/tool-reference/data-management/create-random-points.htm
And then buffer the points.
Or make a fishnet:
https://pro.arcgis.com/en/pro-app/latest/tool-reference/data-management/create-fishnet.htm
and add a numeric field that you calculate with random values to determine "selected" or "not selected":