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Choosing a smartphone based on the operating system on a smartphone comes down to two options: Android or iPhone. Both collect personal data, track activities and track location.
But with Android there's the option of replacing Android with a custom ROM. Will replacing stock Android on a phone with a custom ROM and removing all Google apps prevent Google from collecting any data?
Summing up from the comments:
There's more to it then just getting rid of "Google Apps" – though running a device without them certainly already massively reduces that data collection. A complete elimination can only be achieved by running the device in airplane mode (i.e. not permitting any network connections).
Using a custom ROM without flashing GApps will massively reduce the data collection, yes. But then you also should avoid all apps from Playstore (e.g. by using F-Droid solely), and don't browse websites (only few, like mine, have no Google trackers involved). As @beeshyams already wrote, a Firewall (root: AFWall+ / no-root: NetGuard) can help reducing it further. Getting it to absolute zero is probably only possible by going into airplane mode.
Even if you disable Javascript completely in the browser, there are still Web bugs to consider: tiny, invisible images (1x1 pixel) embedded into web pages for tracking purposes. Websites which are completely free of trackers are rare; at least two thirds of all existing websites integrate at least one (if not more) Google Trackers: Google Analytics, Google Tag Manager (both to be found even here at SE), Google Ads, Google Fonts, miscellaneous Javascripts (ajax.googleapis.com), Google Maps, Youtube, and so on.
TL;DR: You can massively reduce it, but you can't get fully rid of it without breaking stuff. Using a custom ROM without GApps is a good start, avoiding apps from Playstore helps a lot, using a firewall app (AFWall+ if rooted, NetGuard otherwise) helps further. Selectively enable Javascript for websites in your browser (e.g. using the uBlock Origin addon) massively improves on it.
[ EDIT ] Stop your trigger happy down vote finger for a second.
A custom ROM on Android is usually a modification of the factory edition, a port from a different phone running the same kernel and Android version, or a cross-port to upgrade the version by merging needed firmware files with the new release... Sometimes if the custom ROM builder is intelligent enough, they'll build a complete ROM from the AOSP ( Android Open Source Project ) however that usually requires acces to kernel source and most manufacturers don't release this unless required by law...
To define Custom Rom as a modified stock system with proprietary software removed for copyright compliant releases, then IPhone also has custom ROM's ( Firmware ) because you can Jailbreak an iPhone and modify the system to "customize it".
Ok... so, you can build your own custom ROM that is specifically designed to remove any google data collecting software on Android, as Android is an open sourced project, you can modify it to build your own OS if needed ( one with removed google data collecting software ).
However.
As i assume from your question,
" You Don't Want To Be Tracked In Any Manner "
Google has several methods of data collection, for example if you prefer to use Chrome then data analytic software will collect a lot of information about your browsing habbits ( for improvements to the software ) and to be sold to third party data minners .
Even if you don't use chrome and you avoid using google.com and any related websites/companies or softwares you'd still potentially have data collected by other applications and websites that'll sell this information to a global analytics company ( usually AXIOM or AXIUM .. can't remember the spelling ) .. the company release's information back to Google and Google can still " Track " you regardless of your product choice.
For example if you used Facebook, the fact that around 80% of Internet users have Facebook tells me you most likely do... Facebook is also a company that provides personally identifiable analytics to AXIOM, that can and most probably are purchased by Google and nearly any other company working on artificial Intelligence, AI need's data to lean, human slave works to give it some. The start of the end.
Anyway, you Can remove a lot of data collecting software, but it's only going to either increase someone's interest in your device usage ( Google ) or end up causing data to be collected more often ...
For example if you used Purchased software, it'll be constantly logging to Google that you haven't purchased it, this is because it's constantly connecting to Google's servers to check for purchases by your account, and reporting that it can't verify the purchase because it's missing the Google Play Services application.. In time, this should increase someone's interest ( Application Developers - Google - Others )
The question is why ?
If you need to stop it from collecting your habbits, try using alternative methods, like using DuckDuckGo.com ( a search engine that doesn't track you )
Turn off unnecessary data collection in every application that you can
( Sometimes the switch to turn off analytics is hidden in weird pages like help and info etc... )
So to answer your question in one line.
No, Google has other means of personalized analytics
