The outer boundary for a star is the distance where water is not always frozen. The `no-atmosphere' temperature may be below the average freezing point of water, since we expect greenhouse gases to raise the temperature an additional 50K or so.
The inner boundary for a star would be that distance that does not yet heat up the planet so as to put too much water or CO2 into the atmosphere and instigate a run-away greenhouse.
In the graph above, the Habitable Zone is shown as a function of stellar mass. Also shown is the location of our 9 planets. Our Sun is a G star. The only planet in the yellow HZ is Earth. For a more massive F star, Mars would be in the HZ. For a less massive K star, Mercury and Venus would be in the HZ.
Tidal Lock Radius
If a planet forms (or
moves) close enough to its Sun, it will tidally lock:
that is, the planet will rotate at the same
speed it orbits, keeping the same side of the planet towards its Sun.
Our Moon is tially locked with the Earth. If this happens on a planet,
it dismisses it as being habitable, unless it has a very efficient
means to transport heat from the sunny side to the dark side.
From the diagram above, it would appear all M-stars will tidally
lock any planets in its Habitable Zone, meaning M-stars probably
can not support life-sustaining planets.