Examining the QMapControl class, I found that it has neither a sizeHint() overload, nor a resizeEvent() overload. Aren't those functions customarily overloaded for custom widgets?
Not necessarily. Typically, if a widget is used within a layout, the layout will take responsibility for the widget's size. The sizeHint helps the layout do this by providing a recommended size. In the default implementation, an invalid size is returned. The resizeEvent eventually triggers a paintEvent, so my guess is whatever rescaling the map control does is performed in its paint event instead.

I am not sure what you mean by "use it by itself". If you aren't embedding it in a layout or in a resizable parent, it will be created with whatever default size it has, and there isn't any way to resize it except through code. Naked QWidgets don't have size grips. They need to be embedded into a parent that does (QMainWindow, QDialog, etc.)

Sorry for the delay in reply. Something is causing the forum URL to be inaccessible - a DNS problem, DOS attack, don't know. It's been 5 days since I was able to last access the site.