You fresh water tank has no connections with any of the holding tanks. It does have an over-flow/vent, however, that will simply start dumping water on the ground if the tank is overfilled.
I've never heard of the black and grey tanks sharing any connections. I have heard that some manufacturers will route some of the house drains to the black tank, typically a vanity sink in the bathroom. I have also seen posts where an RV owner has modified the plumbing so he/she can divert some of the grey water into the black tank. Typically the grey tank will fill well before the black tank, depending on design, capacities and use.
Jay & Peggy Monroe with Dolly
Can't take it with you - don't plan on leaving any behind
2016 Newmar London Aire 4553, Spartan chassis
Wrangler Unlimited toad