I'm related to David, he's my grandad.
Estoy relacionado con David, él es mi abuelo.
Why is estoy used and not soy?
It seems to me that the relationship is permanent and defining, so I would expect soy to be used.
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As Javi mentioned, a better translation is:
Estoy emparentado con David.
When to use
estar is always difficult for foreign speakers. While the rule of thumb is that
ser is used for something permanent, there are many exceptions that you'll just have to learn using the language.
That said: what about inlaws? That relationship is not necessarily permanent.
As comments state, permanence is not always the key to choose between ser and estar.
When combined with the past participle of a verb, "ser" creates a simple passive, "estar" expresses the state.
Ser casado = Get married, to enter into marriage
Estar casado = Be married, to be in a marriage
This should explain why you need "estoy" in your example.
The explanation is simple. SER is "To be" and when this verb is used we usually are talking about ourselves. The most used form of the phrase you are explaining is "Soy el hijo de David" in which you can see the I am very well specified. ESTAR (also "To be") is mostly used as a verb of staying in, meaning, a continuous action and mostly used for others. Though "Estoy Emparentado con..." is a correct way of saying it, "Soy Pariente de..." is the most widely used. Might be related to the humans egocentric phenomenom and definetly states possession of the other in a way. Philosophically examining it. Now, we usually don't even use it that way either in spanish, we tend to say "David es mi padre" or "Es mi padre" because is more correct to mention the other before us which subconsciously shows humbleness.