Hayley - he is the sole surviving registered owner although all three are still named on the register.
What happens next re the trust and 'the right thing' will depend on what the trust arrangement is and the sole surviving owner is of course bound by the restrictions on the title also.
I would recommend seeking legal advice as appropriate both with regards how the trust works, how it might come to an end and next steps re how it protects the beneficial interests of for example your late Father.