I want to buy Medium guage strings to be able to play drop A songs but still use standar tuning. Will they fit on a Squier PJ?
they will fit, but a 105 string is way too light for Drop A. I use 65/130 strings for BEAD and AEAD (Drop A). I had to re-drill the bridge and modify the saddle for the 130 string.
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Some brands offer taper core 130 strings, like Sandberg (and probably GHS), which would fit.
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That taper is for the tuning machines though, not the bridge. You have to pull the whole string through the bridge holes.
Some do it as well for the bridge side, meaning that they don’t get as thick at that end. I’ll post a picture when I get home 
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Yeah but - you still have to pull the entire string, including the big fat middle, through the hole. So if it is not wide enough, you need to drill or ream it out.
As far as I know, the diameter of a string stays the same for most of its length. Strings tend to be thicker at the ball end for non tapered strings as @Whying_Dutchman shows on his photo of a non tapered string 
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That’s why I ask.
They are thinner at the ball end though…
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Here’s the picture.
The string did fit through the hole. I wouldn’t be sure about the 140 though as it was a close call
And by the way, it’s a standard Squire Affinity bridge.
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funny how long is the taper ! I imagined that the largest diameter of the string was in contact with the saddle already
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It might be difficult to adjust the saddle for intonation with the full width. I fully retracted the saddle and it might still be a little off. Not sure anyone would notice
I already had this case. A solution would be to cut the spring in half (or use another shorter spring) to have a few millimeters more 
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