CC-CV Charging question

I want to build a custom 10S5P battery pack for my build. I want to use the following parts:

50 LG HG2 Cells

BMS:

AAANNNDDDD either one of these power supplies:

OR

I am trying to achieve Constant Current Constant Voltage charging to safely charge each cell to max capacity whilst charging the pack quickly as possible.

Is the BMS responsible for providing the trickle charge of 50-100mA to charge each cell to its full capacity once the cell voltage reaches 4.2V (i.e. by only drawing 50-100mA from the power supply) OR Should the power supply itself be responsible for the trickle current/Constant Voltage charging?

BMS Specs say this: Technical Parameters: Balanced current: 60mA (VCELL = 4.20V when) Balanced for: 4.20 ± 0.05 V

That top power supply outputs 48v. That is too much for 10S. @whitepony may be able to answer your other questions.

Yep but it can adjusted within the voltage ranges of 41-56V it says on the spec sheet so I thought it would be ok.

the power supply is doing the cc/cv switching, a bms just checks if each parallel pack is within 2.5-4.2V (or whatever the bms specs are). im charging since 1.5years with a “link 2” kind of charger, set to 41.4V cv saturation with 4A cc current!

Ahhh right I see. So I should then go in for the 2A charger you think?

I am also building a battery pack 10s3p with HG2 batteries. What charger did you buy? And what BMS did you buy?