Besides the les paul and the ML, what other types of guitars have a similar small neck style?

and also, how can I remove corrosion from the metal parts on one of my guitar necks?
Small in what sense? Thickness, width, length, scale length, etc?
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I believe there are some PRS models with 'small' scales.
To remove any corrosion I tend to find either replacing the parts out right (eg. screws and other disposable parts) or giving the parts a very hard scrub. Last time I used a screwdriver with a rag over the end to get rust off my fret markers, great for getting into the wee nooks and crannies lol
Almost any Gibson, Some ESPs, mainly the ones modeled after Gibsons, Carvin set neck guitars, and every brand pretty much sells some guitars with shorter scale lengths. Some Jackson king V's and Ibanez SZs.
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At first I thought you were asking about the neck-profiles and couldn't figure out why you were listing an LP and ML under the same category lol.

But yes, anything with a 24 3/4" scale is what you're looking for. Most Strat/Superstrat copies are the longer Fender 25 1/2" scale so watch out for them
Endorsed by Dean Guitars 07-10
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[thread="1166208"]Gibsons Historic Designs[/thread]
PRS guitars are usually 25" scales, fender jags are shorter too, and ESP Viper and LP look-alike are 24.75" (can't remember the name, sorry)