Warranty on replacement phones having recently taking my phone into an Apple Store with what was a manufacturing fault,2 months before the warranty ran out they exchanged it without hesitation,
12 weeks on and now the new replacement phone has a number of faults now happening, 
Did the warranty begin again on the new replacement phone or does it just transfer over meaning the warranty ended in January as it would have on the original phone?
The original devices warranty or 90 days, whichever is longer.

A replacement product or part, including a userinstallable part that has been installed in accordance with instructions provided by Apple, assumes the remaining warranty of the original product or ninety (90) days from the date of replacement or repair, whichever provides longer coverage for you.

http://store.apple.com/Catalog/Images/worldwidewarranty.html