Whenever I maximize the Tor browser, it shows a warning:
Maximizing Tor Browser can allow websites to determine you monitor size, which can be used to track you...
How can screen resolution or monitor size be used to track a person?
Whenever I maximize the Tor browser, it shows a warning:
Maximizing Tor Browser can allow websites to determine you monitor size, which can be used to track you...
How can screen resolution or monitor size be used to track a person?
All Tor browser users are asked to surf pages using the default window size. So if you follow this practice, you are just like other users; I mean the screen resolution won't be used as a factor to identify you.
From here, you can read an interesting comment that fits your question:
Using an unusual screen resolution was sufficient to identify me uniquely to panopticlick. With my portrait mode screen resolution of 1200 wide by 1920 high, the default window size of 1000x1765 was unique, no resizing or maximizing needed.
Visit browswerspy webpage that implements a demo where you can find out information about your screen including width, height, DPI, color depth, font smoothing.
Conclusion: do not distinguish yourself from others. Act as everybody else.
Perhaps it's worth mentioning that the impact of resizing your browser on your privacy heavily depends on what window size you set. Maximizing Tor browser on a screen with a standard resolution like 1280x1024 or 1080p is not too bad - lost of people have screens like that, and you probably won't end up being the only one with that resolution. The adversary will still be able to tell that you're running Tor on a desktop PC rather than laptop - those often have WXGA resolution, or something model-specific which is worse if you want to stay private.
The worst thing you can do is to resize the Tor browser manually to a random size instead of maximizing it. The adversary won't have a clue about the hardware you're running on, but you will probably be the only person with that browser size on each site you visit. This means your activity can be tracked - the adversary will know that sites A, B and C were visited by the same person (you), despite the fact that Tor used three different IPs to access those sites.
EDIT: One thing I would like to add here: running a browser with JavaScript support with Tor is something I wouldn't do at all. Screen size aside, JavaScript provides numerous options for tracking. For example, Google is able to distinguish users from bots by the way you click on a button, and that same algorithm could probably be tuned to identify individual users as well.
Client-side code (JavaScript) on a web site you visit has access to screen resolution and other settings. Often the combination of these settings are unique enough to match your current session (which may be protected by tor) with some other session that is not protected by Tor. Following the fingerprint analogy, if you use Tor but have a non-default window size, it can be unique enough that it is like you are leaving a fingerprint at a web site you visit. And with that fingerprint, they can track you to other web sites.
... and just to clarify "track": if you go from their page X to their page Y, they can tell that somebody with the same resolution visited both pages, and maybe with enough information (see @Begueradj answer above) they could even guess correctly whether or not it was the same person.
... and "they" is the web host: If you then go to somebody else's page A, then the process starts over with that new somebody else.
... but they wouldn't necessarily know (from that alone) who that person was. They can't really track you across different web sites (unless they host both sites), and they'd need to piece together with something else to figure out who it actually was. Though the three different IP addresses might tell them it's a TOR user.