It looks like half of the head that broke off is still attached to the tripod. Is there a way to release the parts sticking up from the flat base to which the three legs are attached or a flat base at the top of an extendable center column if the tripod has one?

To raise the center column, loosen the large knob on the side of the part that the three legs attach to and pull the center column up.

There are several possibilities regarding how the part that remains is attached to the center column.

• The cheapest tripods usually have a threaded center column to which the bottom of the head is directly attached. If this is the case for your tripod I know of no source to buy a replacement head with a bottom hole threaded to fit directly on the center column shaft.
• Most tripods attach the head to the tripod via a 3/8"-16 (3/8" in diameter with 16 threads per inch) bolt sticking out of a flat platform attached to either the top of the center column or directly to the spider that the legs are attached to if it has no center column. A few use 1/4"-20 bolts.¹ The head is detached by unscrewing it from the Bolt.
• More advanced tripods use the same 3/8"-16 bolt but also use locking screws to prevent the head from loosening and spinning off during use. If that is the case, the below instructions will allow you to detach what's left of the head from the tripod.

There may be one, two, or three set screws on the bottom of the flat base that will need to be loosened in order to twist the partial head off the 3/8" screw that would be holding it on. Typically these are very small countersunk screws with a hex shaped depression in the middle for a properly sized Allen wrench to fit into which are called grub screws.

A few tripods use grub screws with slotted heads.

Again, these things are near microscopic in size. They're nowhere near as large as they look in the above pictures.

Note: You don't need to totally remove the grub screws from the tripod base, just back them off enough for the head to twist off. They can be a pain to get seated if you back them all the way until they fall out. Be sure they're backed off so that the tips are not protruding through the top of the base before attaching another head. Once you've got another head attached, then tighten the grub screws back in to lock the head in place.

Here's an example from a random tripod viewed looking up from underneath.

For more about how to detach a head from a tripod with grub screws, please see:

How can I remove the ballhead from my Manfrotto tripod?

¹If you get the partial head off and find there's a 1/4" screw instead of 3/8" screw protruding from the middle of the flat platform, you'll either need to use a head that has a 1/4" female hole on the bottom (rare) or use a 1/4" to 3/8" insert (very common) between the 1/4" male screw and the 3/8" female hole found on the underside of most tripod heads. Screw the insert into the bottom of the head fairly tight, then attach the head with the insert inside it to the tripod and twist it down until it's snug. Then tighten the grub screws (if any) from underneath to lock the head in place.