Leaves/grass/weeds etc. I usually just bag. There are certain times of the year (fall I believe) where you can put up to like 10 bags at a time during trash days.

The city does an amazing job with branches/larger limbs at least in my experience. If you place larger limbs/branches into neat piles (no longer than say like 5 feet) at your curb, they bring a large truck with a claw grabber every recycling week and take everything. I feel like I push it too far sometimes at the amount I put out there lol but they always take it.

I just took down a massive tree in my yard and kept most of the trunk for firewood, but I had about 6 massive piles of limbs/branches covering my entire curb and they took every last bit of it