The UK government should undertake an extensive examination of the personal circumstances of your extended family member (s) (including their financial or physical dependence on you) before a decision is made on whether to grant them permission to come to the UK. If your family member is refused permission, the government must give their reasons for the refusal. However, there is no longer a right to appeal against the decision to refuse a residency document to an extended family member of an EEA national.
As extended family members do not have an automatic right to be in the UK, these family members must have the correct permission before coming to the UK. If they are already in the UK with another type of immigration permission, which will expire before the time they wish to leave, they must make their EEA extended family member application as soon as possible, as otherwise they will not have permission to be here (or study) between the time their immigration permission expires and the grant of permission to be here as your extended family member. If there is, or will be, such a gap family members are advised to return to their country of residence to make the application, returning when permission is granted.
If you want your co-habitee to come to the UK with you (or join you here), European Union law says you have to be in a ‘durable relationship’. The guidance issued by the Home Office in interpreting EU law says that you need to show that you have been in a relationship 'akin to marriage' for at least two years. However, it continues on to say: “…there may be instances when the two year rule is not satisfied but the couple have a child together. In these circumstances you can use your discretion if there is enough evidence. For example, a birth certificate showing shared parentage has been provided with evidence of living together.” As European Union law simply says that you need to be in a 'durable relationship', without any minimum length - if you need to challenge the UK interpretation of 'durable relationship', seek legal advice.
If you want to bring parents or other relatives, you need to show that they were members of your household or dependent on you in the country from which they have come before you came to the UK or that they are seriously ill and require your personal care. The test of whether a family member requires your personal care is quite high.