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If your credit file is young, or needs some points, Only Experian that I am aware, offers a "boost", but you have to grant them permission to your bank account to scour for utilities and cell phone payments. This is not offered with TU or Equifax.
The only way a cell phone would affect your score otherwise, is if it were sent for collection.
you can avoid an HP by getting a prepaid plan such as Boost Mobile or Virgin Mobile.
and there are other prepaid plans too.
Not unless you don’t pay your bill. Experian Boost supposedly looks at bills such as phone, rent, etc. to give your score a bump, but in general phone bills have no effect on your credit.