Disputed Ownership - Renters?

[Collin Corrington]

Here's today's question. =)  This is in Texas for any specific legal stuff.

Found a house with an out of state owner (IL).  He bought the house and let family members move in while he lived in Texas.  He was relocated to IL and allowed his family to stay (by the way the "tenants" are illegal aliens, owner is not).  This was right at 10 years ago.  

He allowed them to stay and only ask that they pay the mortgage directly.  About a year ago he refinanced and they stopped making payments.  For 1 year he's been covering the mortgage and is fed up.  He sent them a 30 day notice to vacate.  They lawyered up.  

They lawyer is citing since they were paying the mortgage directly and have made "improvements" (a very bad unpermitted garage conversion and carport) that they have claim to the property. However, there is no written lease in place. 

My thought is, buy the house from him.  Then, just file a good old fashioned eviction.  

Is there anything that I'm missing? I don't think the lawyer has a leg to stand on but I'd hate to get into a drawn out battle and just eat up time. 

Thank you in advance for any insight on the matter. 

[Greg H.]

Making payment directly nor making improvements does not in itself bring a claim of ownership in Texas .  Once the 30 day notice expires, he should evict them as a holdover tenant