Engine cutting out question

Just trying to see if any one else has ran across this problem. At a stop, if you take off a little hard engine cuts out. Also radio and lights kick out too. If you stay in the throttle it will get going again. Lift off the throttle and engine dies out. It happens so quick if the radio did not cut out, sometimes you may not notice. Others times you cannot miss, as it stumbles on its face briefly. This is on a 1989 XJ, 4.0, auto. Any suggestions would be greatly helpful.
Thanks

Fixed, and it was a stupid problem. After replacing crank position sensor, ground strap, and check fusable links, a friend stopped by. Went to show him how it stumbles by power braking and suddenly he is frantic. Says sparks are shooting all over. Turns out coolant return hose support was shorting out the positive battery terminal.