It depends. He's on a cycle now where he does some really massive ones every other day or so. Some of those stay contained in the diaper, all of them so far have stayed within the cover (can't say the same for his sposies at daycare). If the covers are getting stained, try sunning them.
When DS was a newborn, our diapers were always a mess! I think it's just a normal part of having a newborn. Sunning the covers might help, like PP suggested.
Re: Blowouts etc.
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