For context, I’m talking about battery packs with 10-20000mAh capacity.
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It depends upon the battery technology.
For LiPo batteries (the kind used in pretty much every phone) the batteries are rated according to their charge (and discharge) rates. Your typical LiPo battery is rated as 1C. This means that you can charge/discharge this battery with an amperage equal to its amp-hour rating. So a 4000mAh 1C battery can be charged/discharged at 4000mA (4A) safely. This also means that to fully charge a 1C battery it will take 1 hour (this isn’t really true, since only a portion of the charge range can be done at this maximum current).
You can purchase high discharge rate batteries with a C-rating up to 30C (or more). They tend to be smaller batteries, and are popular for RC aircraft/drones where they need the high discharge weight, but don’t particularly need a large capacity. In our 4000mAh example this battery could theoretically charge at a 120A rate (an absurdly high rate) with a theoretical charging time of 60/30 = 2 minutes.
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