Is this normal auto behaviour?

[Ferret]

My previous auto did the following, but I wasnt too concerned as it isnt too noticable with the gas/petrol engines - however the rev up lag on a diesel makes it quite noticable:

From a standing start, there's a second or so delay after the engine power comes up before you feel the full accelleration kick in. Full power only transmits through the gearbox once the engines gone over 2k rpm.
This is shown further by the following : if you sit at a standing start and put the handbrake fully on, the gearbox is quite happy to rev between idle and 2k rpm engine speed, just deflecting the rear suspension with torque. However you just go over that 2k rpm mark and the car starts to push through the handbrake and move.

Once rolling, anything upto 50% throttle causes the gearbox to, say, accellerate from 20mph at 1500 rpm - if you push past the 50% the engine rpm slides up to 2500 at the same road speed, just with a hell of a lot more torque.

The gearbox shifts perfectly at the moment, under full throttle there's no slurring between gearchanges, and no slurring under light accelleration gear changes... so I dont think the box is slipping...

Is this just the torque convertor doing what it's supposed to do, adjusting it's ratio dependant on engine torque?

[icesoft]

...if you sit at a standing start and put the handbrake fully on, the gearbox is quite happy to rev between idle and 2k rpm engine speed, just deflecting the rear suspension with torque. However you just go over that 2k rpm mark and the car starts to push through the handbrake and move.

This would probably show that the stall speed of the torque converter is around 2k RPM

Once rolling, anything upto 50% throttle causes the gearbox to, say, accellerate from 20mph at 1500 rpm - if you push past the 50% the engine rpm slides up to 2500 at the same road speed, just with a hell of a lot more torque.

When you open up the throttle over a certain amount (say 50%), the torque converter clutch will unlock to allow more of the upper RPM horsepower to be converted to low RPM torque through the fluid in the torque converter.

This behavior is by design, perfectly normal.