Window size and window position are in priority controlled by the application itself. Some applications remember their window size, others start with a default. Some applications remember the window position, others not. Then, the window manager decides on the position.
Ubuntu, that by default uses Gnome Shell, uses "mutter" as the window manager. The default placement of windows is controlled by the "Smart" algorithm. That algorithm will tend to place windows in the left corner, and else on another place of the window that is free. If no free space is available, new windows will be placed in a cascading order starting from the left top.
You can change the default placement of "smart" to "center" using Gnome Tweaks. Head to the "Windows" tab to activate the setting. That way, new windows will be created in the center of the screen, unless the application itself overrides it.
Only when using the traditional X11 display manager, you can have more control on where window are positioned upon launch, either with the "Put windows" extension, or —and this works on any desktop running on X11— with one of the venerable tools "devilspie" or "devilspie2", daemons that watch the creation of new windows and size and place them according to your rules.