To build upon Bose-x's statement. The type certificate holder has to be not just out of business - but obviously completely and hopelessly incapable of provding technicaql support.
Hence aircraft like Luscombe's and Taylorcraft are not allowed to transfer in the UK - inspite of the lack of support.
The transfer of Austers was an epic process which although it resulted in a more legally compliant situation limited the 'priveleges' of Auster pilots - for no good reason other than it was convenient for the CAA.
Suffice it to say your C of A airceaft cannot and will not transfer any time soon. Of course the situation pre-1990-ish was very different - but in those days the CAA had engineers not solicitors!