What teachers tell you in school is that as you get close to a uniform sphere the gravitational force increases with the square of the distance to the center of such sphere.

What they don't tell is that once inside the sphere the force decreases linearly, because the planetary mass ahead of you is partially balanced by the mass behind you.

With this you can see that the gravitational pull of a planet/start/spheroid is largest at its surface. So, if something happens to make a start shrink by some factor, the gravity pull at its surface is increased by the square of this factor, even if the mass of the star remains the same.

Actually I believe starts eject a lot of mass when they become black holes, and this is just a Newtonian argument for a phenomenon intrinsically relativistic, but I hope you get the gist of it.

Yeah - a lot of mass gets 'blown away' which really made it even stranger that gravity increased. While I found your explanation illuminating, I still don't see how you can end up with 'more' gravity then you started with? Mass determines gravity right ? not volume ?

It doesn't, it's just a lot denser. A star has a lot of inner pressure from the ongoing fusions inside of it. When these stop or reduce, the star collapses from its own gravity, as soon as its radius is smaller than the event horizon (i.e. the radius at which the escape velocity exceeds the speed of light) you have a black hole.

That's basically what I keep seeing in the documentaries, but it's still not sinking in. For instance, being denser I could see it making a 'deeper' 'dimple' in the rubber membrane demos they use...but it would also be a much smaller diameter dimple, so only things really close and really small could 'fall' into it ?