Black deposits in toilet tank

[user 33245]

I have 3 toilets in the house all of which have a black deposit in the tank. The material accumulates on the right bottom of all the toilets for whatever reason.
It's consistency is similar to graphite lubricant. It causes black streaks in the bowl which are difficult to clean out.

I have a water softener. I do not have a water filter of any type.

A few posts I have found say this might be due to a breakdown of the rubber in the tank. I have lived in the house for 34 years and this is a recent issue - in the last 2-3 years.

Any ideas?

 

[Geofd]

It's possible that your black rubber washers are breaking down ,along with the rubber gasket between the tank and bowl, is it showing up anywhere else??????( Black rubber washers)= tank/bowl brass bolts,+ black rubber washers