How to connect clean power to multiple pins
I think you are confusing multiple pins and multiple supplies.

If a device has 5 Vcc pins and 5 Ground pins, all the Vcc pins should be connected to the same supply, and all the ground pins to the same ground. 

If the device has 5 Vcc pins and 2 Vcc_ADC pins, the latter two could be attached directly to the same place as the 5 Vcc pins, or indirectly to there through some additional filtering.

Each and every Vcc pin should also have an associated decoupling capacitor, or capacitors populated and attached as close to the pin as possible. Additional, more complex, filtering can also be added for sensitive circuits or very high frequency devices.

With this type of component, power and ground planes are much preferred as the pins can connect to the appropriate plane very close to the pin for SMT, and right at the pin for through hole.

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