Since the boostmobile cdma phones run off sprints towers would i have to have coverage from sprint?

or could it run off verizon/alltel/at%26amp;ts network? my mom said she talked to someone at radio shack and they said itd work better when at%26amp;t gets here. i was wondering because im payin $90 for verizon right now and its not worth it|||I had boost and they were bad . Text slow or just didn't send and every text I received had to download and about a quarter of them failed and I text a lot so that sucked . I switched to virgin mobile which is sprint network also and I love it . Got the android phone with 25$ a month with unlimited text and web and 300 min and for 45$ you get the same but 1200 min. 4get boost use virgin mobile|||only CDMA companies like verizon and sprint. att and others use simcards. so probably sprint. but if you use verizon tower it would probably be roaming.