I start car, disconnect battery, switch on headlights, and engine dies.

Is the alternator light illuminated on the dash? Does it go out after starting the car?

Learn something every day. Didn't know a car could run with the battery disconnected, thought it disabled the ignition.

yes light goes out, after starting, but when engine is running if i use eletric windows, with headlight on lights go dom

Once started the car should run with the battery disconnected, but if the alternator was dodgy you would see the alternator light coming on, or the battery wouldnt charge and it wouldnt start.

Get a volt meter on the battery - it should show ~12v without the engine running, and ~13.5v running and charging. If it doesnt show more volts running then there is an issue with the alternator.

The problem you describe could just be a safety feature on the car, without a battery to dampen the current in the system, it may detect a spike, and kill the car so as not to do any damage anywhere else.

check the earth straps and points, also check for voltage drop between wiring

battery is kicking out 12.4v,, and with engine running 14.6v
i have put new earth straps on, and fitted extra.

Then its probably running as it should - normal running wont involve the battery being removed whilst the engine is running

As far as I was aware all electrics are run from the battery nit the apt, if you have fir example an electrOnic choke, lift and fuel pump then yes the engine will die through lack of juice and to too it the distribution cap will be electronic. In new cars fook knows but in old cars it is straight forward

The regulator circuits inside an alternator are designed to "assume" there is a battery connected which in itself acts a as a sort of regulator against peaks and troughs in the output voltage.

The alternator is a rectified AC generator not a DC generator and so does not produce a stable DC output without a battery to "smooth" the supply voltage.

Running without a battery is very dangerous as surge voltages may occur which could destroy the ECU etc.

Presumably when you switched the headlights on, the trough in the output voltage was insufficient to maintain the regulator circuit within the alternator and hence the alternator switched off.