When to leave the propagator

I've sown various seeds in a propagator indoors and they are growing fast. One plant is already to big for the propagator. So I wonder, when and how to move them out of the propagator. Can I just take them out and put on a windowsill or should I take off the lid and let them be? It's mainly the squash and fat babies who are outgrowing their space.
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.