Confirmed this date with the Dealership, wrong battery was installed.
Correct battery should have been a 680 Amp, not 600 Amp.
Battery to be replaced next week.

The original battery (battery size and
type) as indicated in the vehicle's
order specifications must always be
installed to ensure correct operation of
the on-board electrical system!
----------------------------------------
If the vehicle is equipped with an IBS
(Intelligent Battery Sensor), the
battery must be registered via the
diagnostic system (ISTA); this process
also registers the battery with the
vehicle's on-board electrical system.
----------------------------------------
Standard batteries can always be
replaced by AGM batteries with the same
specifications.
Following either type of replacement,
the vehicle registration process in
ISTA/P must be supplemented by a vehicle
coding procedure, which is carried out
as follows:
----------------------------------------
Read out battery size and registration
from onboard electrical system:
ISTA->Service functions->Body->Voltage
supply->Register_battery replacement->
Test plan

Thank you RedRiley !!
I should have more specific with my question.
I recently had my Battery replaced at the Dealership where I purchased the car (new).
The battery that was removed, and that was original OEM to the car, was a 680 Amp battery.
The battery that they replaced it with was a 600 Amp battery.
There is a significant difference in the cranking speed since the change.
Still starts and runs fine.
However, I am just a bit concerned that they made such a change without telling me.
my question is what is now recommended by the manufacturer (Mini).
Problem is that I have been given several sizes that are supposed to be the replacement.
I just do not know what is correct.
 Thanks again......

//bfy.tw/Lfve

looking for correct battery size for 2013 Mini Cooper S with Auto trans and 1.6 liter engine.
any help would be appreciated.