Not parent, but part-time PhDs aren't entirely uncommon (at least in the UK, where I am) and I'm currently supervising one. There are two major difficulties an

Not parent, but part-time PhDs aren't entirely uncommon (at least in the UK, where I am) and I'm currently supervising one. There are two major difficulties and one major advantage over the full-time version. The advantage is that you can work, so students aren't dependent on external funding or an ever-shortening runway of their own funds. This isn't a small thing. On the other side, though, it doubles the length of an already lengthy process (do people really want to be spending 7-10 years of all of their spare time unpaid and lonely?) and increases the chance the the candidate will drop out (in that they keep an alternative on-hand, rather than burning their employment bridges to do it full-time). Given how hard the PhD process can be, simply saying 'sod that' is always a temptation. Anyway, it'll depend on the supervisor and the university. Some have policies against it, others are happy to consider.