My LO has jus started walking independently at 14 months old . Still wobbly .. how long will it take them in General to begin to walk more steadily or even run ?

Give them a little more time. Even my 22mo still stumbles when walking at times. Running will take a longer time as it requires a huge balancing 'skill'. Give them more time.For them to strengthen their leg muscles. soon they will be running and you would wish they slow down!