Is there a maximum mass a star can have?
I don't believe there is a theoretical limit as such. However, there is a practical limit in that, the more mass a star has, the quicker it burns out. At that point it goes supernova and leaves behind something. This something could be a neutron star or a black hole, depending on size.
How about a recent thread?
For Population I stars, the maximum limit is ~100 solar masses since the (normal) main sequence pulsations are so strong as to disrupt and disperse the star. For others, link where turbo-1 suggested.
There is an upper limit because at some point the star will ignite and the stellar wind will begin carrying off the outer protosphere. The upper limit is not firmly established, but, as turbo-1 noted, our region of the universe caps out at around 200 solar masses. Theoretical models suggest stars formed over 13 billion years ago could acquire even larger masses due to low primordial metallicity - approaching 300 solar masses.
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