Nearly all construction and household debris loads normally. The limits come from the regional landfill's acceptance rules and from what the City will and will not handle.
Celina's own rules put heavy material squarely on the property owner. Brick, broken concrete, lumber, dirt, automobile frames, discarded tires, dead trees and tree limbs are all listed as the owner's responsibility to dispose of, not the City's. The City's residential cart service will not take construction debris, tires, wood or excessively heavy objects either, and its collection arm is limited to 100 pounds of lift. A roll-off is the practical answer for any of that.
At the regional landfill, tires are accepted only up to a 24.5 inch diameter and loader, farm tractor, motor grader and scraper tires are refused outright. Hazardous waste, liquids, paint, solvents, fuel and asbestos stay out of a standard container anywhere.
Shingles are accepted but surcharged, so they are best kept separate. If you are unsure about an item, raise it with your account manager before it goes in.