Bonjour,

you are right, both are correct. The first version (“souhaitant”) being more literate.

Please note that to be grammatically correct, both versions would need a comma between your two sentences:

Je viens d’acheter un domaine, son ancien propriétaire souhaitant s’en débarrasser rapidement.

Je viens d’acheter un domaine, parce que son ancien propriétaire souhaitait s’en débarrasser rapidement.

or

Je viens d’acheter un domaine. Son ancien propriétaire souhaitait s’en débarrasser rapidement.

Yes, both examples mean the same.

The first and the second example you have given are both right.

However, I think that there is a little difference between each one.

The second case is generally used to explain (Parce que) what you did in the first sentence. For example you would say : J’ai acheté une maison parce que je voulais être propriétaire. It is the direct reason why you bought an house, you wouldn’t buy an house because someone want to sell it but you buy an house because you want to buy one.

Don’t hesitate to comment if you need more explanations.