80mm lathe chuck, 3 or 4 jaw

[Jonathan]

I have no idea what self centering is anyway, I know nothing about lathes.

Self centering means when you turn the chuck key all the jaws move at the same time. They're generally used when it's not critical to have the part concentric after taking it out of the chuck and putting back in, since most will only be repeatable to a few hundredths of a millimetre. If you do need to hold the part with virtually zero runout, then a 4-jaw independent chuck can be used as you can move each jaw separately and use an indicator to get the part on centre. They're also good for holding irregular shaped parts, but take longer than self centering chucks to set up.

Which is why I was searching ebay for a mini one :) I think its time I got one rather than using the router in funny ways.

It's surprisingly not much more money to get a decent size lathe, and they perform much much better, so if you have the room it's worth considering.