Different potentials always try to equalize  to the same potential thus there will be current flowing between the two (or more). It will  always use the path of least resistance.

Because parasitic current is not only a single frequency like 50/60Hz but a band of frequencies we need to consider not only resistance (DC) but impedance (AC) which makes it even more complex.

The goal of correct grounding is to give different potentials in different audio components a path of least resistance to earth ground so that it wouldn't flow through the interconnect and cause hum or buzz.

Power cables have impedance and that's why it is not a good idea to connect the earth ground of two or more lines in the breaker box. The ground of the  interconnect might be an easier path for the current.

One dedicated circuit and all audio components connected with short and low impedance power cables in one power strip for digital/one for analog  to the outlets of a good power conditioner would fulfill most necessary conditions.

It can have different reasons If one doesn't hear any hum or buzz. Sometimes the potential difference is so small that it isn't audible (you got lucky!). Or the sensitivity of the speakers is too low. But as long as some currents are flowing through the interconnect there is a modulation of the audio signal and depending on the strength it will have some neg. effect on the SQ. If an audio system should theoretically sound better than it does (considering the expenses and efforts) I would always start measuring potentials and consider correct grounding.

Different potentials always try to equalize to the same potential thus there will be current flowing between the two (or more). It will always use the path of least resistance.

The current will take any path that is provided...

As for using more than one dedicated circuit, to feed audio equipment where signal feeding other equipment is by wire interconnects, in most causes where there is a ground loop hum problem the reason is the wrong type of branch circuit wiring was used and or the method of installing the branch circuit wiring was done incorrectly. Another problem can be the dedicated branch circuits were not fed from circuit breakers connected to the same Line, leg, in the electrical panel.

FWIW, I have two dedicated branch circuits that feed my 2 ch audio system. One for the analog equipment the other for digital. I installed 10/2 with ground NM cable, (Romex is a trade name). Length of the two runs are 75ft each. My system is dead quiet...

The OP’s three 12/2 NM cable dedicated Lines are 35ft each. IF he installed them correctly he shouldn’t have any problems at all.

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The article form E. Juaneda which I posted earlier really explains the problem of possible ground loops. Anyone who is interested to understand causes and how to fix it will find the answers there.

'The current will take any path that is provided' but like in any voltage divider  more current will flow through the branch with less resistance. If that's the interconnect  it will still cause a problem.

@apogeum Wrote:

One dedicated circuit and all audio components connected with short and low impedance power cables in one power strip for digital/one for analog  to the outlets of a good power conditioner would fulfill most necessary conditions.

See article below, Middle Atlantic Products, Inc.

Power Conditioning
“Power Conditioning” is a very misused term, with no industry standards to allow adequate comparison. Numerous products are
marketed to “cure” AV system noise, lock-ups, reboots and various power quality issues. Many of these are sold partly by fear, partly by
swindling and mostly on misleading “education” that lacks any basis in accepted engineering principles, meaningful data or realistic
demonstrations.
Some people may install power conditioners because they are led to believe that “conditioned power” will improve the way the system
sounds or looks. However, except in rare and extreme situations, these attributes are determined primarily by the quality and
topography of the safety ground system and the integrity of the signal path of interconnected equipment, not by the quality of the AC
utility power.
Two examples of such extreme situations where power conditioning may make a difference include:
- when power is fed from a utility source that is shared by a nearby user of industrial machinery that injects high levels of RF
noise, such as some welding equipment
- when using electronic equipment with cheaply made and poorly designed power supplies, instead of higher quality equipment
that provides adequate noise rejection.
Most power conditioners are essentially low pass filters that are designed to attenuate high frequencies. However, for AV systems,
problematic noise frequencies are under 25 kHz and are essentially unaffected by power conditioners, whose filtering action is typically
effective only at frequencies over about 50 kHz.
The following common problems result in many undesirable situations, including hum, buzz and noise in AV systems, none of which are
solved by power conditioners:

Power Conditioners do not solve
any of these common problems

What actually does solve them

Effects of ground loops (hums, buzzes & video hum bars) Single-point reference ground (can be derived by an isolation transformer), balanced
interfaces, heavy braid shields on unbalanced signal interfaces (keep shorter than 3 ft.),
twisted power conductors
Power line common-mode noise Shielded isolation transformer
AC magnetic field induction (hum & video roll bars) Coaxial cables or twisted conductors within signal and power cables; separation of signal

and power wiring bundles
Cross phase coupling (doubles hums & buzzes) Same phase power
Shield current induced noise Heavy braid shields (instead of signal cables with drain wire)
Pops, clicks and noise from arcing contacts AV equipment powered from dedicated branch circuits, local arc suppression devices at

the appliance or switching device

Control system lock-ups UPS, surge & spike protection, single-point reference ground, avoiding AC electromagnetic

induction into control wires, opto-isolators for long RS-232 links

Hissing at loud volumes during quiet passages Tiered gain structure; higher quality equipment

39 Integrating Electronic Equipment and Power into Rack Enclosures © 2002-2010 Middle Atlantic Products, Inc.

The System Approach to Power Quality