Just asked my 11 year old GS how he saw me, and he looked nonplussed! I suggested "Strict, batty, fair, affectionate" he grinned all over his face. We cook tgoether and do all sorts of conspiratorial things together. We have jsut come back from the supermerket (!) where I got new pans - but I also got him a (totally unexpected) new X-bos game. He loves me unconditionally often bringing me presents when he goes on holiday, rather than his mum or nana. I am the paternal GP but have had him to stay with us, sleeping with me "until I'm 16" for years... I love him to bits!
The 2 GDs are more complicated. the relationship with DD and SiL is a bit iffy at times, though not bad. GD1 loathed me to start with and could barely tolerate being in the same room. She has changed her mind - and I can do "anything" for them now, anything they don't know or can't do, I'm now consulted; so things look up! Still very "strict, batty, fair, affectionate".
BTW I climb trees better then they can, and I'm pushing 70!