Do apple watches work with iphones that are with the boost mobile carrier?

Are you referring to the Series 3 GPS + Cellular? If so, see this for the currently supported carriers. Apple Watch - Carriers - Apple

The watches are not locked to particular carriers, however the carrier has to support the watch. Check with Boost Mobile to see if they support it, as there is generally a fee from the carrier to have the LTE on the Watch.

Otherwise, the regular Apple Watches will work with your iPhone, regardless of the carrier, since it uses the phone for its connection. What the Watch will do when the paired iPhone is not nearby, see this. How to use your Apple Watch without your iPhone nearby - Apple Support

Hi

There are different versions of Apple Watch:

Apple Watch - Compare - Apple

A compatible model of iPhone is required in order to set up and use all models of Apple Watch, including for managing and syncing with the Apple Watch over time:

• Apple Watch Series 3 (GPS + Cellular) requires an iPhone 6 or newer model of iPhone running the latest version of iOS 11.x.
• Apple Watch Series 3 (GPS) and all other Apple Watch models requires an iPhone 5s or newer model of iPhone running the latest version of iOS 11.x.
• Set up your Apple Watch - Apple Support

Apple Watch Series 1 and Series 3 (GPS) and other models

Apple Watch Series 1, Series 3 (GPS) and other models except Series 3 (GPS + Cellular) - see below - do not have built-in cellular capabilities.

Any calls or data-related services are routed either via the paired iPhone or via a direct connection between the watch and a compatible Wi-Fi network (when the watch cannot connect to the paired iPhone via Bluetooth).

Specific support for the Apple Watch is not required on the paired iPhone's cellular plan. These models can be used in conjunction with a compatible iPhone and a service plan for the iPhone from any carrier.

Apple Watch Series 3 (GPS + Cellular)

In respect of calls and data usage, Apple Watch Series 3 (GPS + Cellular) also always first tries to use the Bluetooth connection to your iPhone (which does not require a separate plan for the watch) or, in the absence of that, any available connection to a compatible Wi-Fi network.

If neither of those is available, then Apple Watch Series 3 (GPS + Cellular) has a built-in cellular capability that, under certain circumstances, can enable certain features, which are not available on GPS-only models, to remain available when the watch is used without the iPhone nearby.

In order to be able to use the built-in cellular feature, you would require a carrier service plan for your iPhone that specifically includes support for the Apple Watch, including the carrier first activating the device on the plan:

• Set up and use cellular on Apple Watch Series 3 (GPS + Cellular) - Apple Support
• Use Apple Watch with a cellular network—Apple Watch Series 3 (GPS + Cellular) only

Apple's list of supported carriers is linked below- note that Boost Mobile is not currently listed (in either the US or Australia) and that prepaid plans are not currently supported:

Apple Watch - Carriers - Apple

Apple Watch Series 3 (GPS + Cellular) can also be used without enabling the built-in cellular feature, in which case it functions like a GPS-only model and can be used in conjunction with a service plan for iPhone from any carrier - which can also be a prepaid plan - with no need to activate the watch on the plan.

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The functions that are available on your Apple Watch when it is away from your iPhone depend on various factors including:

• Your Apple Watch model:

  Apple Watch - Compare - Apple

• The features of your carrier service plan:
  • Apple Watch - Carriers - Apple
  • Make a call with Wi-Fi Calling - Apple Support
  • Make calls over Wi-Fi
• The type of connectivity that is available to your Apple Watch at the time:

  About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support

Features and requirements that apply under various circumstances are detailed here, including within the footnotes:

How to use your Apple Watch without your iPhone nearby - Apple Support